The Xbox One's Snap mode looks to be the key to the console's party chat setup, which a member of the Xbox Live development team explained in a post on Major Nelson's blog today.
You'll be able to get a quick view of the parties that you and your friends are in — as well as the games you're all playing — by taking a look at your Xbox Live friends list. From there, you can easily join friends' parties (unless they're private). You'll also be able to jump directly into an online game if a party is open and there's space for another player in the match, as long as the game determines that you're suitable for the game; that's accomplished with the Xbox One's Smart Match system, which assesses factors such as your skill level and playing style.
Smart Match and the party system combine for something Microsoft calls Party Scout, which allows you to multitask while you're waiting to get into a multiplayer game. You can use Snap mode to continue to watch TV or Netflix, for example, and the console will send you a notification when the game is ready for you to hop in.