That's an old and immensely complicated question, to which there is no single answer. Innumerable factors have been advanced by various historians, with better or not-as-good evidence to back them up, ranging from economic crisis and inflation, to climate change and demographic shifts, to political instability and civil war, to loss of support from the elites and the common people, to such old (and discredited) canards as barbarisation of the army and decadence or decline of Roman virtues.

I'm personally partial to views such as Goldsworthy's that the emperors over the centuries made choices seeking to increase their own short-term security and limit the potential for usurpers, at the expense of their empire's longer-term ability to protect its provinces from outside encroachment, raids and invasions, to the point where it became much more attractive for those on the periphery to side with local power-centres or invaders than to remain loyal to an ever-weakening central government. This then undermined said central government's ability to pay for its army and project its authority, sending it into a downwards spiral from which the eastern provinces (sort-of) recovered but the western did not.

I give my best summary of various views I know in this thread, which includes internal as well as external explanations. There's also some interesting discussion below my posts.