The Miiverse is Nintendo’s attempt at social networking via the Wii U console. It’s basically a redesigned Mii Plaza in which you can send messages and status updates to friends on your Wii U friend’s list; or in other words, a Facebook/Twitter like client on your video game console.
The redesigned Wii Plaza shows all the little Mii’s huddled around different Wii U titles showing what games your friends and other Wii U players a enjoying. According to the information from the Pre E3 livestream, the Miiverse is browser based so your 3DS, PC, and mobile devices should be able to connect and share. Unfortunetly the Miiverse will not be available at launch of the system with a release date of… in the future.