What does it mean to appeal a court decision

An appeal is when someone request their case to be looked at by a higher court.

An appeal means that one of the parties is requesting that the decision in your case be looked at again by a higher court. In other words, they are arguing that something went wrong with the first decision and that it should be changed. In most cases, the appeals process is somewhat limited. You probably aren't going to have to go to court again, and the appellate court (the one reviewing the decision) is probably going to give a lot of deference to the already-standing decision.