The after school ballet class has three levels. As your child reaches each level, they get a new dance move they can show off. Somewhere along the way at a random point, they will get an opportunity to participate in a dance competition, at which they can win a trophy for being the best. After they reach level 3, they will get the opportunity for the awards ceremony/recital. Both the competition and the awards ceremony are done on their own time, but there is a time limit to get them done. For the awards ceremony, they will have to go back to the school that same night as their final after school meeting, or the next day.
Learning ballet using the dance barre is for everyone from child aged and older. They will learn the same dance moves as at the after school club, and if you have them in the club and use the dance bar, they will reach level 3 for the club very quickly, which kind of spoils the whole after school thing. However, it takes 3 after school meetings to reach each level, so a total of 9 to master the hidden skill. So if my children aren't going to make it to enough club meetings before they age up to teen, due to missing meetings because of illness or field trips, I will use the dance barre to make up for those missed meetings.
Edit: One other thing - while your sim is exercising at the dance barre, they will get athletic skill and strength training time, but it takes much, much longer to master the dance skill. And once they have mastered athletic, there will be no skill progress meter above their head while they work out at the barre. But the skill they've gained will be added, and you'll get notifications as they gain levels, but not until they've finished the workout that gained the level for them. So it looks like nothing is happening, but it is. You just have to be patient.