In all the centuries since the Bronze Age and war as we know it, did it really take until the 1930s to invent the idea of hitting the other side relentlessly? What was different and new about blitzkrieg?
First of all, 'Blitzkrieg' was a term invented by Western journalists. The Germans themselves never really used a general term for the style of warfare they used in Eastern and Western Europe 1939-42, the closest thing one comes to it is 'schwerpunkt', meaning 'focus point'.
The German tactics describet as 'blitzkrieg' was to concentrate dedicated armoured and mechanised forces, closely cooperate with the air force and punch through the enemy lines and then drive deep into the enemy rear to keep the enemy off balance and create pre-ww1 battle conditions and be able to flank, encircle and annihilate enemy units without slugging it out against strong static lines as ww1 had been.
Static warfare had dominated the western front in ww1, due to several factors. Firstly, due to good infrastructure, primarily railroads, but also roads, the defenders could move reinforcements to a threatened sector much quicker than the attackers, depending on horse-powered supplies and artillery to advance over the taken area to continue the advance, could move. Secondly, the massive armies made a continious front possible, so manouvre warfare and flanking attacks or encircling manouvres became impossible.
The British and French response to this was the set piece battle, where they drew together supplies, dominated the battlefield with artillery, used new artilly tactics (such as rolling barrages, pin-point barrages, pre-calculated defensive barrages and so on), overwhelming firepower of their infantry (with LMGs and mortars becoming increasingly common towards the end of ww1) to methodically dominate the battlefield with fire and destroy any force that tried to oppose them. They did this very well during the last 3 months of ww1, usually referred to as the 100 days offensive, recapturing nearly all French soil lost during the war before the armstice on the 11th of November.
The Germans had developed a different method, where they would use 'stosstruppen', small forces of veteran soldiers equipped with the best the Germans could supply them with (SMGs and LMGs) who would make pinpoint assaults, ignore strongpoints and advance on the depth to attack the weaker rear forces of the enemy, causing cofusion, sometimes panic among the enemies.
So, the allies took back the set piece battle as the wining tactic of ww1 and set out to improve it. Strong concentrations of infantry and artillery, well supplied, with superior artillery and superior firepower would methodically destroy the enemy front, occupy, move up, rinse and repeat to win the war.
The Germans on the other hand experienced their best results using their 'stosstruppen' tactics on the western front, and in large scale offensives with continued movement on the eastern front and worked to combine these during the inter-war years.
Rommel, serving with the 'Alpenkorps', the German volunteer mountain troops aiding the Austrians against the Italians stosstruppen-like tactics to great success during the Caporetto offensive 1917 and wrote about it in his 'Infanterie greift an!' ('Infantry attacks!', meant as a command or urge) and taught as an instructor at the Dresden infantry school where he did his best to infuse this ideal in his pupils 1929-33.
At the same time, a general debate on the armoured experiences of ww1 and how to use tanks in the next war was raging in Europe, where men such as Lidell-Hart and de Gaulle argued for specialised armoured forces capable of operating on their own. In the end, the British and French went with a dual system - slower and more heavily armoured tanks in tank brigades to support the infantry for classic set piece battles and faster, lighter tanks in dedicated mechanised/armoured units to exploit breakthroughs or be quick and fast reserve units to deal with enemy breakthroughs.
The Germans, inspired by Guderian and his book 'Achtung - panzer!' ('Attention, armour!') instead concentrated all available armour and mechanised forces into not only armoured divisions but also armoured corps intended to be able to operate independently on the depth beyond enemy lines, advancing far and hard. This 'deep battle' idea had been discussed and tried in various places, including the Soviet Union during the 20s, but it was only the Germans that eventually adopted the concept whole-heartedly.
The German army had during the 20s under General von Seeckt developed 'auftagstaktik', a concept where higher command would not bother with details and let lower command deal with situations as they saw fit as they had the information on the ground. Higher command would give an order (take village A, cut the enemy supply road B, encircle the enemy force C, relieve friendly force D from enemy attack, retake position E from the enemy and so on) and leave the details up to the lower command. Lower commanders were also allowed to operate without orders or even in contradicton of given orders if they saw oppurtunities or options appear or that was not obvious to higher command. This gave German units a very high flexibility and initiative.
What was new about 'blitzkrieg' and how the Germans adopted it?
The Germans developed the idea that armoured and mechanised forces should be concentrated in one single attack ('schwerpunkt') to achieve a breakthrough and include all combat elements, all motorised or mechanised, to operate independent of regular infantry and artillery dependent on horse powered transport. They would also be able to advance deep into enemy territory on their own in division or corps size.
The Germans had a high rate of flexibility and initiative through 'auftragstaktik', allowing them to use opportunities and situations that set-piece battle tactics did not allow for.
Close cooperation with the air force and the air force having a dedicated force for close air support of troops, in many senses replacing artillery support for the troops advancing on the depth.
'Blitzkrieg' was developed based on German experiences in ww1 and the general debate on how to use armour and air support that emerged during the 1920s and on profilic writers and instructors such as Erwin Rommel and Heizn Guderian. It was specifically designed to break the static trench warfare and allow classical German or Prussian manouvre warfare concepts such as flanking and encircling that they had used in the 18th and 19th centuries.
The idea of "Blitzkrieg" as a military strategy is itself contraversial. The term came into use primarily with Western media, and it was never used by the Wehrmacht. Moreover, several German officers, such as Kurt Student, have asserted that what the Allies described as "Blitzkrieg" was never a systematic strategy at all, and was instead a series of ad-hoc solutions to highly specific problems that presented themselves at the time.
That said, the strategies employed by the Wehrmacht, whatever we call them, were novel at the time. Far more than simply "hitting the other side relentlessly," the "Blitzkrieg" was characterized by concentrated armour formations punching holes through enemy lines through concentrated assaults, allowing mobile and armoured forces to encircle enemy troops and, with extensive aid from air support, liquidate the surrounded pockets. This style of warfare is only really applicable to modern warfare, since it requires that there be a continuous front line for the armour to punch through, and as such it can't be applied to bronze-age warfare.