First of all, we must remember that there was no one Roman religion. Instead, the Roman Empire included all sorts of religions from the official Roman religion that worshipped the Olympian gods, through the "mystery cults" to Christianity.
With regard to the official Roman religion, the two basic features were that it was non-exclusive and it was a religion that might be called transactional. It was non-exclusive in that believers were free to believe in other religions. They could believe in and worship other gods so long as they did the things that were required by the state religion. It was transactional in that it was based on the idea of people and the gods both keeping up their parts of a bargain. All that was expected was that people would observe certain rituals. If they did so, the gods would reward them in certain ways. There was no expectation of personal faith or personal attachment to any god or gods.
These are two of the most important features of Roman religion.