In a nutshell, it was the collapse of a money economy supported by taxation, one which could pay for permanent bureaucrats and standing armies. In the post-Roman aftermath, power was all about control of land. Land, unlike money, can not be hoarded in the same way without engendering serious resentment in a world where land was power.
Thus the early medieval era required kings to constantly grant out land in order to secure loyalty. By the high medieval era, the ability to revoke land given out was lost to the kings as well, thus cementing a significant amount of local noble power. With the collapse of a money economy, nobility became the administration, except that the key difference between a bureaucracy and an aristocracy, is that you can fire people in a bureaucracy and replace them, as they're dependent upon leader patronage. Not so with an aristocracy, who still retain their independent bases of power.
It took the late middle ages and the early modern era for kings to claw back the right to have ultimate power (and ability to revoke) back to themselves. Its also not a coincidence that this power came back concurrent with the economic resurgence of western europe in the guises of the 12th century and 15th century renaissances.
Adding to /u/bitparity 's answer, a very good case example in the struggles of middle age royal houses as they attempt to build a strong state is that of France.
A look at the chronology of French royal demesne illustrates this well. During Hugh Capet's reign it consisted only of scattered possessions around today's Paris, Orleans, and several other domains. Through marriage, they gained claims to the County of Flanders and Duchy of Burgundy within the next several generations. However, the County of Vermandois, which surrounds Hugh Capet's domains, was still separate from France and it took the Capetian a long while to gain control of it.
Aquitaine was gained in the early 12th century, but lost when Eleanor of Aquitaine, Duchess of Aquitaine, separated from Louis VII of France and married Henry who became King of England. This set the stage for the Hundred Years War.
Another important milestone is that of the Fronde, during which first part the Parlement of Paris rebelled against increased taxation as Louis XIV and Mazarin tried to centralize the control and logistics of a royal state army.
A key aspect to this is relative continuity of French royalty, from the Capetians to the Valois to the Bourbons and their cadet houses. To contrast, German kings didn't have such continuity, and thus the Holy Roman Empire didn't become the centralized kingdom that France did. There's a very good recent thread on this subject that you should read:
http://www.reddit.com/r/AskHistorians/comments/2ayc9q/why_did_the_holy_roman_empire_become_a/
can one of you guys go into some detail on how the roman system of delegating their lands in the west to incoming tribes is part of the reason of the downfall?