There are the Charizards (my personal favorite), Horizon, Waterfall, Ocean and Solid Blue.
How did he/she/it put the Yveltal as the background?
I want to know how and where I can get more backgrounds.
(Thanks TheCanadianWifier for making that video)
This video says pretty much. There's a chrome addon called "Stylish" which lets you easily install themes and skins for many popular sites one of those being showdown. There are also some ones you can install very easily. (I'll link one site who has some of those)
You can also read this.
This site has some themes you can install easily. (One of these are the Yveltal one you wanted)