A teacher may oust you from class if you are being disruptive, or you might oust your class president from her position if you beat her in the election. To oust is to “expel,” “kick out,” or “remove and replace.”
When you oust someone, you are “giving them the boot.” A sports team is ousted from a tournament if they lose an elimination round. Oust often implies both removal and replacement. The automobile, for instance, ousted the horse as the preferred means of travel. Likewise, when a politician ousts someone from office they are taking that person’s place in office. And if you beat the all-time record in a hot-dog eating tournament, then you oust the previous record holder from their position.