The Competition Center is where you put all the hobbies and skills to a test to see if you can win fame and fortune in the arena!
Chances are this will be one of the latter structures you build in your town - and it will be very expensive to build! On the plus side though, assuming you have been actively working the hobbies and have at least one Sim who has mastered each, it will serve as an excellent destination for you to obtain bonus XP and wealth...
Each day will bring you a new Competition, and each Competition will require you to commit the Sim that is competing to a 24-hour event.
An example of the Competitions is the Ghost Hunting Competition, which features the following prizes:
1st Place - Gold Medal - 3 LP Prize
2nd Place - Silver Medal - 1 LP Prize
3rd Place - Bronze Medal - $1000 + 1000 XP
4th Place - Steel Medal - $500 + 500 XP
Each day will feature a randomly selected Competition, and once you select a Sim to compete, it starts a 24-hour timer, and your Sim will be unavailable to you until the timer runs out.