Racing games involve multiple vehicles racing a number of laps. They can be realistic or arcade-y, but the end goal is always the same: crossing the finish line first.
In multiplayer racing games it is vital to have as precise information about the position of other clients as possible. The server and the players both need to know details like if its possible to overtake in a curve, if players bumped into each other, and even more importantly - who crossed the finish line first. We need to have server authority, but each Client also needs reliable predictions about where the other players are.