An appeal in formula 1 is when teams and drivers get penalties from FIA, they can appeal to present new evidence. They have to show that they did not break any rules and that the steward made a wrong decision by giving them a penalty.
An official hearing will be held and the penalty will be upheld or reduced. Even though technically the appeal process exists, it is quite a slow process. The quickest appeal process was sorted in a week and the longest was in months.
Recently in the 2021 Abu Dhabi Grand Prix, Mercedez decided to appeal after Hamilton lost to Verstappen. However, later they withdrew the appeal following a statement by FIA.