Gibbon basically said after finish a book about Middle Ages that he had described the triumph of barbarism and religion.
Now regarding Rome itself, Gibbon theory says that the roman spirit was gone, they were no longer warriors at service of the state, instead they were not interested on the state. Actually, most soldiers during the late Roman Empire were just mercenaries, and the pretorian guard was the real power behind, because they were the one who choose the emperors.
Christian religions made romans to be interested more in the Heaven instead of Earth, and at the same time they had several internal disputes about religion.
That's basically what Gibbon said about the end of Rome: lack of civic duty, pretorians and religion. Barbarians were just the coup de grâce.