What did the title, princeps, mean in Roman culture?
Princeps, from which the word "Prince" derives was the title which Caesar Augustus gave to himself. The full title was Princeps civitatus, meaning "first citizen." Augustus used this title as a means of demonstrating that he was on a par with other Roman citizens, not above them. Another Latin phrase which would suit his purpose: primus inter pares, or "first among equals."
Augustus had hoped to restore the old Roman Republic, but knew this was impossible. He also was painfully aware of the fate of his uncle and adoptive father, Julius Caesar, who was assassinated due to rumors that he planned to become Rome's first king. Augustus took this title to dispense any rumors of any pretense of becoming king. In addition, he wore the same clothes as ordinary Roman citizens and lived in a modest home.
Princeps standing alone has no real significance other than as noted above.