The most obvious answer is that the Roman army fought Rome's wars. This is important to state, because Rome was almost constantly at war. We only need to think of Rome's war with Carthage and her immediate war against the Hellenistic East.
The Roman army also built many projects. They, of course, built military weapons, but they also built roads and bridges. This was a quite a feat, because some of the roads and bridges are still in use today. The Roman army also mined for resources. In short, they functioned as engineers.
The army also colonized new territories and Romanized them at the same time. For example, the ancient city of Philippi was settled by Roman veterans.
If we move forward to the empire, at one point the Roman army became so powerful that they were able to elect their generals to become emperors.
In conclusion, the Roman army was more than a fighting force; they also built Rome, spread Roman culture, and even elected emperors.