Okay kiddo, so primogeniture is a fancy word that means that when a family has kids, the oldest one usually gets a special treatment.
Let's say, for example, that your grandpa is a king and he has three sons: Uncle Bob (who is your dad's older brother), your dad, and Uncle Tim (who is the youngest). If primogeniture is in place, then that means Uncle Bob would be next in line to become the king after grandpa! Your dad and Uncle Tim would have to wait their turn.
Basically, it is a rule of inheritance that says the oldest child gets to have certain things before their younger siblings. This could be anything from money and property to social status and titles. It has been around for a really long time and used to be common in many countries.
However, nowadays, many people believe that it's not fair to just give everything to the oldest child. Some countries have gotten rid of primogeniture and now it doesn't matter who is the oldest.
Does that make sense, sport?