The court is your profile within the game. Players can see the name of your Lord/Lady, as well as your might, number of cities you have and what alliance you are in. You can decorate your court by paying gems (real money) for various court items.
When you visit a friend's court, or the court of someone in your alliance, it will allow you to execute various actions, which will yield a small bonus of your choosing.
An example of such activities::