Religio Romana is Latin for the Roman Religion.
At least, that's what some people would have you believe. Religio does not actually mean religion – in fact, the Romans had no word like our religion. Religio is more a word meaning duty, or honoring the gods with piety and the correct ritual actions.
I think…Roman Reconstructionism is a better term.
Like other Reconstructionist paths, the Religio Romana is an attempt to reconstruct the practices and religious customs and beliefs of an ancient culture, or of one no longer practiced today. In RR, one can choose from different time periods, all with their own views of the Roman deities – the Archaic era, the Republican era, the Empire, even Byzantine Rome.
Unlike Christianity – which many people come to paganism from – the Religio Romana is an orthopraxic religion. That is, it has its focus on the correct ritual actions and words, and belief doesn't matter nearly as much as in Christianity, which is an orthodoxic religion.
Do ut des: Latin phrase meaning "I give so that you might give". This essentially sums up the reciprocity that is the basis for worship of the Roman deities: if you want something from a deity, you need to give Him or Her something. It's like…an eye for an eye, only not in the violent sense. I've seen the Religio described as a contract between a car salesman and a prospective buyer.
Mos maiorum: Latin for "the way/custom of the ancestors", this is basically reconstructing the Roman virtues – of which there are many, and most of them fit well in today's society. This also includes venerating the family spirits and ancestors.
Pax deorum: the "peace of the gods". The Roman deities were generally seen as benevolent, but if you majorly messed up a ritual and didn't apologize or try and redo it in some way, you might invite their wrath. So the peace of the gods is attained by giving offerings in the correct manner and not neglecting worship.