The term "pagan" is typically used in modern times to refer to anyone who believes in a polytheistic religion. Therefore, we would say that the Greeks and Romans were pagans because they believed in many gods. We would also say that the ancient Celts were pagans because they believed in gods and spirits and such. So the term really covers a wide variety of beliefs, from religions like those of the Celts and of ancient Shinto Japan to much more formalized religions like those of the Romans.
These beliefs differ from Catholicism most clearly in the fact that they are polytheistic. Catholics, like all Christians, believe in one God only. In the context of medieval Europe (since you tagged this with "medieval") a pagan might also believe, for example, in spirits that brought good or bad luck to harvests or child-bearing or animal rearing. None of these would have been officially acceptable to the Catholic Church.