XP stands for Experience Points.
The more XP a player or a horse has, the more experienced they are.
The more XP you have, the higher level you are, and there are some benefits of being a higher level:
  -   Horses get more skill points and can breed.
  -   Players can buy more horses and have access to more game features.
  -   Both players and horses have a better chance of winning shows.

Players get some XP at the time of entering shows. All other show earned XP for the player and horse come when the shows run.