So there are two basic reasons for this, one of which was strategic and one of which was political. They sort of tie together, but not entirely.
After Italy invaded Greece in October 1940, the British reacted by sending forces to support the Greek Army, pursuant to their defensive agreement that had been concluded in 1939 (which committed the British to intervene against any threat to the territorial sovereignty of Greece or Romania). The combined British-Greek force was able to resist the Italian invasion, which, like some of Italy's other recent military campaigns, was disastrously mismanaged and disorganized. This created two problems for Hitler, one military and one political.
From a military perspective, the presence of British troops in Greece (including the island of Crete) was problematic. British bombers stationed at airfields in Greece would be able to reach the oilfields at Ploiești in Romania, which were essential to the German war effort because they provided between a quarter and a third of all of Germany's oil. Romania wasn't technically in the war yet at that point, but it was going to participated in the upcoming invasion of the Soviet Union, for which Germany had begun positioning its forces months before the Marita. Forcing the British out of Greece did prove to be important in this respect, since the Romanian oilfields were out of range for all Allied bombers until the capture of the airfields near Benghazi in Libya in 1943; even then, it was at the very, very limit of the range of the USAAF B-24s that participated in the disastrous raid on the refineries in Ploiești and Câmpina on 1 August 1943 (Operation Tidal Wave). Romania only became the target of regular Allied bombing missions after the capture of the airfields at Bari in early 1944, by which point Romania was only a few months from being knocked out of the war by the Soviets anyway.
In addition to the Romanian oilfields, the presence of British forces in Greece was problematic in other respects. The Western Desert Campaign had been ongoing for almost a year by the time of Marita, and the airfields in Crete in particular were important for the British forces in Egypt. The Western Desert Campaign was vital to maintaining the Axis' strategic position in the Mediterranean because it allowed them to suppress British shipping via the Suez Canal, and if the Allies could push the Axis back into Libya and get more forces and supplies through the canal, it could lead to the total collapse of the Italian forces, which had already proven their vulnerability. An Axis collapse in North Africa could allow for a direct Allied attack against Italy, which was (correctly) seen as the Achilles' heel of the European Axis. Of course, this is what eventually happened, after the Allied victory at El Alamein and the capture of Northwest Africa in 1942, so Hitler was right to be fearful of that outcome. This concern made it necessary for the Germans to evict the British not only from mainland Greece but from Crete as well.
Of course, the threat to Italy posed by the failure in Greece and the shaky situation in North Africa wasn't just a military problem, it was also a major domestic political issue. The failures of the Italian military had a significant effect on public opinion toward Mussolini's regime, potentially putting his political future in doubt. Hitler was afraid that a decisive Italian defeat could lead to the overthrow of Mussolini's government and the complete withdrawal of Italian forces from the war; again, this did eventually happen in 1943, so Hitler's concerns here were rational. The combination of military and political threats to Italy and therefore to the Axis as a whole were enough of a reason for Germany to take the time to invade Greece, along with protecting its vital oil supply for the upcoming invasion of the Soviet Union.
Hitler later blamed the Italian failures in Greece, and the subsequent need for Germany to invade Greece, for the failure of Operation Barbarossa, claiming that it had delayed the launch of Barbarossa for several weeks (from the original start date of 15 May 1941 to the actual start on 22 June). However, most historians are skeptical of this argument, and Hitler's own generals noted that the main reason for the delay was the weather, not the invasions of Greece and Yugoslavia. Historians have also noted that starting on 22 June would've been sufficient for Axis forces to reach their objectives prior to the onset of winter if Hitler had made the correct strategic decisions (i.e., to focus on Moscow as his generals urged, rather than breaking off the advance toward Moscow to mop up Ukraine), so Hitler's claim that Greece caused the failure of Barbarossa is generally considered to be blame-shifting, rather than a serious argument.
The German attack on mainland Greece was highly successful (to the point where it exposed Churchill to substantial criticism for sending British/Commonwealth forces there in the first place, even though the majority of Commonwealth troops were evacuated successfully) but Crete proved to be a Pyrrhic victory due to heavy losses among the German paratroopers. Of course, most of the fears that motivated Hitler to invade Greece ended up coming to pass anyway. The Axis forces were defeated in North Africa; the Allies invaded Italy, causing Mussolini's regime to collapse; and the Allies used European airfields to bomb Romanian oil production facilities (although the strategic significance of these attacks was relatively minimal), so the strategic logic behind the decision to invade Greece was probably sound, even if it just delayed the inevitable. The lessons, kids, are 1. don't ally with Italy and 2. don't invade Russia.
Sources:
Antony Beevor, The Second World War (Back Bay, 2012)
John Keegan, The Second World War (Penguin, 2005)
Gerhard Weinberg, A World at Arms (Cambridge UP, 2005)