This is a good question.
First, Rome was on a policy of expansion. They expanded to such a degree that there were many borders to defend. As early as the reign of Diocletian, it became apparent that the Empire was in need of reform on account of its size. In light of this, the sheer size of Rome necessitated more man power. In time, there were not enough citizens.
Second, the Romans always had a problem with the Gauls. Caesar did an admirable job, but it was only a matter of time before the "barbarians" to the North would come down. When they did, the question was what could Rome do with them. One answer was to use them in the army. Hence, they became mercenaries (and to a certain degree, Romanized).
Finally, the Roman Empire weakened over time. This meant that they needed more people, because an entire citizen army (like in the Republic) was no longer possible. The many civil wars in Rome were partially to blame for the inability to field a citizen army.