The Miiverse is a "Mii universe" that is the system's redesigned networking and designed Mii Plaza.
Miiverse the new network service where Miis from around the world can meet. The redesigned Wii Plaza shows Mii clustered around various Wii U titles. This shows what games players are enjoying and what's popular. Nintendo also showed Miis leaving in-game messages.
Mii WaraWara, taken from the Japanese's "warawara" (the sound of things happening, in Japanese).
Even when the game isn't designed for online or even if the game's are not online, the Miiverse can still connect consoles and players. Think of it as a social networking system for the Wii U, the 3DS, and even your mobile device or PC.
A Nintendo spokesperson clarified that Miiverse, the Wii U's mainscreen, will be available from the day the Wii U goes on sale. However, the ability to access the Miiverse from 3DS handhelds, PCs, and mobile devices will come at a later date.