From this writer's point of view, I love being able to be playing a game, press the Home button, and post a screenshot of where I am stuck and a post asking for help, and within mere moments or minutes receive a helpful response. This is especially terrific for games that do not currently have any online guides, particularly new and/or more niche games. The community gets to assist one another. It doesn't even have to be for gameplay advice either. For example, I probably never would have been interested in getting Trine 2: Director's Cut or Mighty Switch Force: Hyper Drive Edition without the suggestions from the Miiverse community.
Something else that makes Miiverse special is the ability for developers to have a new and much more direct avenue to keep in touch with their fans. Toki Tori 2 developer Two Tribes' Collin van Ginkel notes that he and his team will be able to contact fans via a home console setting, something that has never been done before.
Miiverse is a bastion of creative users, and while some can say that Wii U owners/Miiverse participants are only doing great works of art and browse through Miiverse because they have no games to play (in my case that was true), the Miiverse community is still a bustling one.
Right now I'd like to share the amazing artwork of various Miiverse denizens, including yours truly (though I would not classify my stuff as "amazing"). The skill that these artists show off is just simply insane.