Miiverse is the first thing gamers will see when they boot up the Wii U but it’s not just an interface. According to Satoru Iwata, it’s a “social window” that “links player to player, living room to living room”. This is a concept that’s deeply integrated with the entire Wii U experience in multiple ways.
Firstly, via the above interface, you will be able to see the games people are playing from around the world. This includes games you do not own, exposing you to what’s popular at the moment. (You can see how Miis are clumped around various icons for games.)
There’s a messaging system with Swapnote-like functionality. You can type messages, but also draw on the screen. Alongside the messages you’re also able to change the expression of your Mii to better convey your mood. This system will be accessible via the PC and any internet-enabled mobile device at some point in the future, but that particular functionality won’t be available at launch.
The last big feature is that all games can integrate with Miiverse. This allows even single player experiences to be given a sense of connection by, for instance, making it possible to see messages from other people around the world while playing a game. This was shown in the context of New Super Mario Bros. Mii, with players leaving behind notes at the end of a level.