Have you played the game, Overwatch?  It's a game produced by Blizzard.
No, but I know it came out on all platforms in May 2016.
You really need to try it.  It's a 6 versus 6 shooter game and you can choose different classes within the game. 
Is it anything like Destiny where there is PVE and PVP?
It's solely PVP, there is no PVE content. It's gotten a lot of attention recently and even has it's own e-sports league.
Oh that is cool. So you are competing against another team of real players then. Sounds fun.