Upon defeating the Pokemon League and becoming the Kalos Region Champion (!!!), you will be fight AZ immediately, but you most likely already knew that. Besides this, you can catch some legendary Pokemon, explore new areas, go on sidequests, and more. You can-
- Battle AZ
- Get a second starter from Shauna (a level 1 form of the she picked)
- Receive the National Pokedex
- Go to Kiloude City. Here you can use the Friend Safariand the Battle Maison
- Upgrade your Mega Ring
- Get a Pancham hat if you're a boy or a Sundae hat if you're a girl
- Get the Poke Radar
- Go on side quests with Looker
- Catch one of three of the legendary birds (depending on which starter you chose)
- Catch Zygarde
- Catch Mewtwo
Here's the source I used.
Other than that, you could start to fill up your Pokedex or restart your game and do a fun challenge like Nuzlocke or there's this one new challenge some users have been playing. It has something to with Avatar, but whatever.
Hope I helped even a little bit. :]