Roman society during the Pax Romana was very complex indeed, but also very unique.
The Romans still worshipped their gods, Jupiter, Mars, etc., just as they had for many centuries. Religion was a very big part of Roman life. Often people would be compared to gods, for any good or bad reason. Honor was defined as doing a good service for the gods, something in their favor. Therefore, many Romans strove for such glory in the eyes of the gods.
Society was also flourishing due to the many advances in technology that the Romans made. With running water, public baths, and othe public entitites, society was at an all time high of peace and prosperity.
The Pax Romana was the longest period of peace and prosperity that Europe has ever known.