It's not about watching tv and gaming "at the same time" it's about having all of your living room entertainment connected and instantly available to you.
For example. You're flipping through channels and nothings on. You get a game invite from your friends. In the past you wouldn't know about this invite until you decided to turn your console on the next day. With Xbox One you will be notified immediately, and since you don't have to worry about switching discs, no matter what game they invite you to, you can jump directly into the lobby and start playing.
Example 2: your watching the lakers game, they're getting blown out so you decided to play halo. Halfway through the 3rd quarter Kobe gets hot, you get an alert and instantly switch back to the lakers game. When the game is over Halo is sitting and waiting exactly where you left off
There are plenty more examples to go over, but I think you get the point now.