The appellee is the person who won the case in the lower court and now must defend that win against the other side's appeal.
In an appeal, the party who lost in the trial court (the appellant) asks a higher court to reverse or change the decision. The appellee is the party who prevailed below and responds to the appellant's arguments, urging the appellate court to uphold the original ruling. The term appears in the case caption and throughout the appellate briefs.
If you are the appellee, your job is to show why the lower court's decision was correct and should stand. This matters because the appeal shifts the burden to you to defend the outcome you already won, and failing to respond effectively could lead to losing that victory.
Many people mistakenly think the appellee is the one bringing the appeal, but actually the appellant is the one who initiates the appeal. The appellee is the one who responds to the appeal, not the one who started it.
Get the actual rule
This page explains the concept. When it matters to your case, read the rule that governs it in your court — we hold Texas, federal and Washington court rules word for word, and every state's official resources are on the state pages. If someone cites a case at you, check that it exists first.
Related
General explanation, not legal advice, and not specific to any state — procedures and deadlines vary by jurisdiction and court. If you can get a lawyer or free legal aid, do: every real option.