To joust is to fight against someone, usually using lances, on horseback. Such a contest is called a joust.
If you've ever seen a movie or TV show about medieval times, you might have seen two knights jousting. This is a sport that takes place on horseback and involves lances, which are long like spears. The knights charge each other and try to hit each other with the lances and knock each other off the horse. This type of contest — which usually involves a tournament — is called a joust. Jousting is as old as the Middle Ages.