I've heard more than one story as to the why, and I don't know if what I know is up to date or right. I've also understood that not much is known about the period right after, and I wonder if that's still true.
My favorite current theory (before anyone drops Demandt's list of 210 reasons) is de-globalization.
These are the lines you can read inbetween Chris Wickham's seminal book, "Framing the Early Middle Ages." The long and short of the argument is, the material culture and social structures that underpinned the Roman Empire as we understand it in colloquial terms (i.e. not its Byzantine political continuation or its supposed Germanic inheritors) depended upon a complex economic integration between the main drivers of the Mediterranean economy, namely the grain shipments between Africa and Rome, and Egypt and Constantinople. This regular grain shipping allowed other trade to piggy back onto it, promoting a sea-wide system of bulk transport that would be more difficult in a land based transport system. The "globalized" sea trade also allowed for intense specialization of regional economies which would boost overall wealth that the elites in power could spend on material manifestations of their wealth, i.e. art and architecture.
When, for a variety of reasons including military defeat, this sea-based transport broke down, economies became intensely regionalized, poorer from a material standpoint, but also at the same time more autonomous.
The long and the short of this theory being, when it comes to material culture, complex bureaucratic and aristocratic structures, these are based primarily upon an ability to generate/extract/redistribute efficient wealth from the resources of their territory. With the loss of that territorial control and redistribution network, the structure of the empire fell, even if the political leadership continued onward (as was the case in Byzantium).
Now, this is only one of... so many reasons. So many. Its my favorite reason because it's timely to our argumentation now, when the debate is precisely over whether the world economy should be globalized and regionalized. The "fall" of the Roman Empire offers a useful example of the last time the world deglobalized in a major way, and the result of which is neither positive or negative overall – it is positive or negative depending upon whether you benefit from it.
Because at the heart of Wickham's ideas, is that this material wealth is extracted off the backs of the poor 90% of nobodies. What you lose in material, you gain in regionalized and personal autonomy, with less state influence. Even now, this is a microcosm of debates within our current politics (which I wont get into lest I run afoul of the rules). If you're willing to accept more "relative" poverty, you can gain in autonomy. But of course, in a modern capitalist world, that is never the case, because I don't know about you, but I like air conditioning.
Which is all to say, history offers interesting examples, but there are an unlimited number of them. So the answer to your question, what's the best understanding? We don't have "best" understandings. We have "new" understandings, all of which can be deployed for a variety of informative purposes, depending upon your own particular purposes.
I like de-globalization because it's informative to our current world, and a bit contrary to the standard message. We are, after all, a society that enjoys novelty.
The brief answer isn't so brief, firstly because Rome changed and endured for so long, and secondly because one needs to consider the manifold outside disruptions and very significant inside stresses.
Over its agitated history in both the Republican and Imperial periods Rome faced down quite a few existential crises, and also came back from devastating losses while safeguarding or discarding modes of life and systems of government - they worked more often than not until not.
So what's Rome's biggest success? According to "Pax Romana" by Adrian Goldsworthy, it would be gaining the buy-in of so many disparate peoples. See the trajectory of the Gauls, once regarded as a terrible threat to the city - yet its nobles after the fall of the Empire actually served to instruct barbarian kings in Roman law.
The dangers were many and varied, and sometimes slow to develop. To the East, the Parthian and its successor Sasanian Empire [centered around modern Iran] often loomed as a threat with comparable resources.
Once Rome chose to turn its back on Europe's big, hostile forests to the North ["Varus, return me my Legions"], those barbarians didn't vanish, but rather over generations multiplied and drew nearer - for both trade and plunder and maybe also safety, while testing the effectiveness of defenses in growing groups. Rome quite adroitly organized its point and mobile defenses and played a long diplomatic game with the nearer tribes to keep the peace and maintain them as a buffer.
As an example of the geographic reach we're talking about, Roman coins were found on Sweden's biggest island Gotland - which became one of the Vikings' chief trading centers later on. Then again, inside the borders, a legionary from Syria could and did serve in Britannia's far north.
But as serious internal strife too often weakened the later Empire, outside mercenaries gained both access and more intimate knowledge of Roman ways both literally and figuratively, also acquiring quality Roman weapons.
You could say internal coherence was signally lost when the Goths, seeking shelter, forced their resettlement as an undispersed whole inside the borders - this was unprecedented, if I remember correctly, and the beginning of the long end. They went on a rampage soon after.
However, speaking to bitparity's view, it's only later that the Vandals plundered their way through Hispania and crossed over to Mauretania in North Africa, finally ending an important source of grain supply centered around ancient Carthage [Africa Proconsularis] - the other being Egyptus.
It's really very difficult to see into the dark years between the end of the Western half of the Roman empire and the rise of primitive literate civilization long after. People living in Europe used to think giants had built the ruins in their midst.
Peter Heather in "The Fall of the Roman Empire" has done the hard work of presenting excellently informed speculation pertaining to the matter at hand.
It would take nearly a thousand years for curious souls to begin systematically reacquainting themselves with that distant past. Interestingly, there's another collapse of Mediterranean civilization we know far less about that took place about 1'500 years prior to Rome's.