In two words: Getting paid.

In more words: Initially, Rome followed the same model as the Greek City-states; the wealthier, landowning class (Citizens) performed all military duties. This was a practical matter, as soldiers had to provide their own arms and armor. There was also the notion that "Only those with a hearth have the right to defend it." Renters were thought of as transients, and it was believed you couldn't trust them to stand fast in battle--they had nothing to lose but their lives.

However, towards the end of the republic, this system started to be insufficient to deal with the needs Rome's increasingly aggressive expansionism. At the same time, the landowning class was becoming proportionately smaller as small farms were replaced by massive latifundia, while masses of people were flooding to the city proper. In 107 BC, a general named Marius reorganized recruitment, removing the requirement to personally supply arms and armor as well as the landowning requirement. In the place of what basically was a citizen's militia, a professional army developed. Without a farm to return to, the lower classes could become full-time soldiers--tremendously increasing both the size and capabilities of Rome's legions abroad. They earned a decent wage doing so. In addition, in wars of conquest, soldiers shared in the victory of their general--along with the glory and social stature, they got a slice of the physical booty. Captured slaves, gold, jewelry, and perhaps most importantly, land in the new province were distributed to victorious armies.

To sum up, a Roman soldier in Britain in AD 43 was likely an enlisted man who joined up to make a living and, ideally, get rich. This was often motivation enough to fight and die all over the world.