What/Who in the world is うーたん? She is a character on the NHK show いないいないばあ, a popular program for toddlers. My daughter looooved (and still loves) watching this show. The show uses cute characters to teach basic things like colors, simple songs and dances, potty-training, etc.
Go here to read more about the show.
Here is a blog about Uutan. It has a lot of YouTube videos.