Being familiar with the way a dance looks & memorizing the basic structure of the dances can be very helpful to a feis musician in staying focused while playing at the feis.
In Irish dance there are different levels of competition: beginner, advanced beginner, novice, open/prizewinner, preliminary championship, and championship. The names of categories vary by region. There are also special categories for adults.Dancers advance levels by gaining medals in different dances. The dances include jig, Hop jig (single jig), treble jig (hard jig), slip jig, hornpipe, traditional set, reel, nontraditional set and treble reel (tipping reel). This thread on dance.net explains them in a bit more detail. This blog is also helpful.
In a feis a variety of soft and hard shoe dances are performed and individually judged.