Josip Broz, commonly known as Tito, was certainly one of the more skilled politicians of the last 75 years and an important figure in European and international politics. While I would contest the direct connection between his death and the break up of Yugoslavia (I'll get to that), it is undoubtedly true that Tito was one of the more important figures of the Second World War and the post-war era in Europe.
Tito was born most likely in 1892 (birth dates vary mainly because Tito had been very careful about his public image once in power and not knowing his exact age was part of his projected mystique) in Kumrovec in what was then Crotia under Austro-Hungarian rule. Working as a metal worker in the 1910s, he was drafted into the Habsburg Army in WWI and fought on the Russian front where he became a POW in 1915. Released during the February Revolution in 1917, he went to Petrograd where he eventually joined the Bolshevisks (he had been a member of the socialist party in his homeland before). Subsequently he fought in the Red Army during the Russian Civil War.
He returned to Yugoslavia in 1920 and was active in the Communist Party. Because the KJP was illegal in the first Yugoslavia, he was imprisoned because of political agitation several times and also through work for the party and his connections to the Comintern and Moscow voted into the Central Committee of the Party. From 1936 to 1938 he was a Comintern agent in Paris, responsible for smuggling Yugoslav volunteers into Spain for the purpose of fighting in the Spanish Civil War. He, through either luck of connections, survived the Stalinist purges of the Comintern parties during that time and after the KJP had been hit particularly hard by a bloody purge from Moscow was made the leader of KJP in 1937 because he was known as good, loyal party soldier in Moscow.
Being an illegal party the KJP was necessarily conspiratorial and had only a small number of members throughout Yugoslavia in 1940. Tito would have most likely remained a rather inconsequential figure in the grand scheme had it not been for the Axis invasion of Yugoslavia in 1941. Despite contrary orders from Moscow (who until June still retained its position influenced by the Molotov-Ribbentrop pact), once the Axis invaded Yugoslavia in April, Tito and the party began preparing for resistance and once they got the go-ahead from Moscow in June, they were able to strike incredibly effectively right away.
Over the summer of 1941 a coalition between Tito's communist Partisans and the remnants of the Yugoslav Royal Army reorganized as the so-called Chetniks were able to wrest control of almost the entirety of Serbia from the Germans. The German Army in Serbia was by August 1941 confined to a small number of Urban Centers and the situation got so bad that there were voices within the Wehrmacht that advocated ceasing control of the country and re-invading at a later point. Now part of this was related to the very thin German troop presence in Serbia but it was this early that Tito made a couple of important choices that would eventually majorly contribute to the Partisan's success in Yugoslavia:
First of all, through his previous contacts with people who fought in Spain, he was able to organize a very effective guerilla army.
Secondly, he decreed that the declared parole and goal of the Partisans was national liberation and not socialist revolution. Of course there was no doubt that the movement was controlled by the communists but in their rhetoric aimed at peasants etc. national liberation was always their declared goal. And they didn't limit themselves to one nationality (unlike the Chetniks who were a Serbian movement) but rather embraced the liberation of all Yugoslav peoples thus attracting people as diverse as Slovenians and Macedonians, Muslims and Roma into their movement.
Thirdly, he proved quite adept at playing one occupying power against the other, namely Italians against Germans. The Partisans negotiated both ceasefires and passages through Italian occupied territory several times in order to more effectively strike at the Germans. This tactic was initially not popular int he movement but it was largely thanks to Tito that it prevailed and it paid off several times.
In 1943 with only tacit support from Moscow, Tito and his communist party was able to pull off another very important victory. The foundation of the Anti-Fascist Council for the National Liberation of Yugoslavia, nominally an umbrella organization for all fighting against the occupation but really controlled by Tito and the communists, established a new Yugoslav government under Tito that the Western Allies at least partially recognized as such. Over the further course of the war, the Partisans swelled in numbers, ending the war at 800.000 fighting men and women.
After the end of the war, Tito and the now renamed KPJ set to work to pacify Yugoslavia under their rule and establish a Stallin-style socialist dictatorship, including the violent suppression of their political enemies. The Stalinist period of Yugoslavia lasted until 1948 when the Soviet-Yugoslav split occurred. Major factors in the political split between the USSR and Yugoslavia were the support of Greek communists in the Greek Civil War by Tito, which had been rejected by Stalin – for more context see here –, the talk of a Bulgarian-Yugoslav Federation and generally Tito's independence from Moscow, which he could afford because his leadership of the Partisans in WWII and the liberation of Yugoslavia with hardly any help from the Red Army had lead to Tito having a mythical status among Yugoslavians.
After the break, Yugoslav socialism and politics needed to be readjusted. The most important elements introduced under the leadership of Tito were:
in internal politics, the principle of "brotherhood and unity", meaning that within Yugoslavia all the various republics were to peacefully coexist and unlike in the first Yugoslavia no part of Yugoslavia would reign supreme over others.
within Yugoslav socialism, the principle of worker's self management. Unlike a Soviet style planned economy, the KPJ decided that their socialism would consist of actually turning over the means of production to the workers. Companies and plants were to be managed democratically by the workers who would elect representatives in order to decide on company and plant policy. While this was not radically implemented, it lead to the establishment of pockets of free market within the Yugoslav economy.
within international politics, a policy of neutrality between the blocs. This importantly enable Yugoslavia to profit from Marshall Plan Aid from the West and invest heavily into its economy laying the ground for becoming the only socialist country with a considerable consumer goods industry that exported into the West.
While this international policy initially lead to great fears in the Yugoslav leadership that the Soviets would invade (in 1952 there were talks of a Yugoslav-Greek-Turkish defense pact, which would have made Yugoslavia practically a member of NATO), it later transformed into the formation of the Non-Aligned Movement, attempting to establish a third bloc between West and East. While the NAM never gained the importance Yugoslavia wanted it to have, Yugoslavia's neutrality between the blocs brought a very advantageous position: It profited from Tourism from both West and East and also could trade with both.
These successes together with the mythical status of Tito from his time in WWII and a noticeably cult of personality that developed in Yugoslavia established Tito as the central figure of Yugoslavian politics. Incredibly adept at internal politics, Tito was heavy handed when necessary and backed off when he saw it as opportune. He firmly planted himself as the center of all Yugoslavian politics. And in 1980 he died.
I have written about important factors for the Yugoslav break up just today here and while I won't copy paste it all here, the importance of Tito's death lies in that the people who had served under him basically treid everything they could to what has been described as "Tito without Tito" meaning to continue what they saw as what Tito would have done without possessing his adaptability and political cunning. The linked comment goes into more depth concerning the break-up but that is the short of it.
Sources:
Holm Sundhaussen: Jugoslawien und seine Nachfolgestaaten.
Jozo Tomsevich: War and Revolution in Yugoslavia, 1941–1945: Occupation and Collaboration.
Stevan K. Pawlowtich: Hitler's New Disorder.
Follow up question: how do historians generally regard Tito? I've heard some people praise him for both doing his own thing and preventing the ethnic tensions of Yugoslavia from becoming a full war (as it did in the 90's). Do historians agree with that sentiment?
I don't think his death was specifically a cause of the break-up of Yugoslavia, but it certainly didnt help. It would probably be fairer to say that Tito was the reason Yugoslavia stayed together. He was a rallying figure that citizens loved (so much so that it gave birth to a later movement, Yugonostalgism).
Tito maintained a policy through the communist party of aversion towards nationalism and nationalist groups, citing them as "dangerous to the state." As u/commiespaceinvader points out, he comes up instead with a policy of brotherhood and unity that grants equality to all ethnic groups and republics within Yugoslavia. Tito's time spent as President (up to roughly 1968) was centered around navigating the complexities that come with having constituents made of nationalities with very little in common other than constant fighting. After 1968, Tito begins to slowly remove himself from the responsibilities of daily politics in Yugoslavia, culminating in reforms introduced in the Constitution of 1974 that remove the responsibility of governance from the federal government and grants it to the republics. The federal government existed as an oversight to ensure the collapse of the state could be avoided, but by and large, the responsibility of day to day governing fell to the individual republics.
That, I believe, is a stronger case for the break-up of Yugoslavia. Republics began using their responsibility to look out for their own interests, rather than the interests of the entirety of the state. This grants more strength to larger republics like Serbia and Croatia over that of smaller ones like Montenegro or even autonomous regions like the Vojvodina. Tito's death exacerbated this and actually left a power vacuum since the Constitution of 1974 ended the office of the Presidency. This vacuum allowed various ethnic tensions to grow unchecked, which is a backdrop of the break-up.
I would say the actions of Slobodan Milosevic, his takeover of Serbia in 1987, and his ethnic wars in the 90s would be more of a cause than Tito's death.
Sources: Mocnik, Nena. Tito's Flawed Legacy: Yugoslavia and the West Since 1939. Boulder, CO: Westview Press, 1987. Pavkovic, Aleksandar. The Fragmentation of Yugoslavia: Nationalism and War in the Balkans. New York, NY: St. Martins Press, 1997. Pedro Ramet. Nationalism and Federalism in Yugoslavia, 1963-1983. Bloomington, IN: Indiana University Press, 1988.
Edit: Added sources for my answer. Was on mobile initially
Further to the superb points that have already been raised, I would like to raise the factor of Tito and his long-term failure with Yugoslavia's economic policy.
As has been previously alluded to by others, Yugoslavia's foreign policy was closely linked to its financial policy. The "West" (mainly the U.S.) pumped vast amounts of capital into Yugoslavia after the 1948 Tito-Stalin split in the hope that they could gain a foothold in the "East". And after Khrushchev's rebuilding of Soviet-Yugoslav ties, investment soon flooded in from the East too. (I won't go into the detail but it's relevant to note that Yugoslavia, aside from straddling the East/West tightrope, had become a founding member of the non-aligned bloc in 1961 and so that altered some of the previous closeness between foreign and economic policy).
I don't believe that Tito's death was the cause behind the breakup of Yugoslavia, but certainly Tito's actions had virtually destroyed the position of relative economic strength that the country enjoyed during the earlier years of Tito's reign. By the time Tito died in 1980, Yugoslav debt had risen to a substantial sum of $18.9 billion. The joke that I gather was told in Yugoslavia during the funeral was that the only reason so many foreign dignitaries and heads of state turned up was so that they could collect the payments on the debt!
Factors such as nationalism, ethnic hatred and governmental instability were (I believe) symptoms of the problem. Although interestingly you could argue that foreign intervention was the cause behind Yugoslavia's breakup, but I'll leave that for another day!
Hope that helps, Sam (A-level history student, studying the breakup of the "first" and "second" Yugoslavia).
Sources: -John R.Lampe: Yugoslavia as History: Twice there was a country
-Susan L.Woodward: Balkan Tragedy: Chaos and dissolution after the Cold War
-Kate Hudson: Breaking the South Slav Dream: The rise and fall of Yugoslavia