Mumble Happy Feet is the nickname of Mumble because his tapping feet that he called "Happy Feet". He is known as the worst singer in history (actually, he can't sing).
The "Happy-Feet dance" is a sort of claqué or american tapping, but with a kind of latin style (Like the movements in which there is a lot of bold body contact that he made with Gloria, while she was singing Boogie Wonderland). It's very difficult to describe, since Mumble can dance at the rhythm of every song and singing style (From the british rock to the South-American mambo).
Mumble is a male emperor penguin who can't sing, but he can dance instead. He uses his tap-dancing to literally sing with his body. Mumble was known as an outcast, because after trying to do the mating ritual with Gloria dancing, he embarrassed himself in front of the community with his "Happy Feet" and was banished from the territory. Then he found the aliens, but they put him in a zoo. There he attracted their attention by dancing, and the aliens released him in Antarctica again to see if there was more dancing penguins. When Mumble returned to Emperor-Land, he tried to make everyone dance. The other penguins didn't believe in Mumble at first, but after seeing the tracking device on his back (after this device started to do some weird noises) the others began to dance with him. An alien search party arrived to Emperor-Land in a helicopter and witnessed the whole event. The alien's leaders declared a ban on Antarctic fishing activities, and the fish started to come back to Emperor-Land's shores. Mumble is transformed into a hero and is nicknamed "Mumble Happy Feet".
Gloria also calls Mumble "Twinkletoes", but in a lovingly way.