Princeps senatus was a person who was the leader or chief of the Senate, which was a group of important leaders and lawmakers in ancient Rome.
Think of the Senate as a club for the most important people in Rome. They would meet together to talk about important decisions that affect the country. Just like you might have a leader or the "captain" of a club, the Senate had its own leader, called the princeps senatus.
This person would be chosen by their fellow senators to be in charge of leading the meetings, making sure everyone was heard, and making sure the discussions stayed on track. They were usually very respected and important people in Rome, who had proven themselves to be wise and fair in their decisions.
So, imagine you are part of a club, and one of your friends is chosen to be the leader because they are very smart and always make good decisions. That's kind of what the princeps senatus was like in Ancient Rome!