O-Powers are time specific bonuses introduced in Pokemon X and Y which when activated grant players abilities like a higher change of critical attacks in battle, easier befriending of Pokemon, etc. O-Powers in the game are found by talking with the “O-Power guy” dressed in a pink suit, talking to him will have him give you an O-Power.
You can use multiple O-Powers at the same time but you need to keep an eye on the Energy bar, each O-Power uses Energy so the more you use at once the lesser time you’ll have before they expire. O-Powers can be accessed on the right page of the PSS.
There are 14 O-Powers in total and can be found in the following locations (thanks /u/thedragonguru):
You can also level up O-Powers which can be done easily by using them. So use O-Powers as many times as possible to get the greatest benefits from them. Also make sure to use them on your friends and Acquaintances , trust me they’ll thank you later.