Every emperor penguin sings a unique song called a "heartsong" to attract a mate. If the male penguin's heartsong matches the female's song, the two penguins mate. Norma Jean, a female penguin, falls for Memphis, a male penguin and they become mates. They lay an egg, which is left in Memphis' care, while Norma Jean leaves with the other females to fish. While the males struggle through the harsh winter, Memphis briefly drops the egg. The resulting chick, Mumble, is unable to sing but can tap dance. Nevertheless, he is enamored with Gloria, a female penguin who is regarded as the most talented of her age. One day, Mumble encounters a group of hostile skua, with a leader who is tagged with a yellow band, which he says is from an alien abduction. Mumble narrowly escapes the hungry birds by falling into a crevice.
Years later, a young adult Mumble is ridiculed by the elders. After being isolated during the graduates' song, he is attacked by a leopard seal. After escaping, he befriends a group of Adelie penguins called "the Amigos", who embrace Mumble's dance moves and assimilate him into their group. After seeing a hidden human excavator in an avalanche, they opt to ask Lovelace, a rockhopper penguin, about its origin. Lovelace has the plastic rings of a six pack entangled around his neck, which he claims to have been bestowed upon him by mystic beings.
For the emperor penguins, it is mating season and Gloria is the center of attention. Ram贸n, one of the Amigos, attempts to help Mumble win her affection by singing a Spanish version of "My Way", with Mumble lip syncing, but the plan fails. In desperation, Mumble begins tap dancing in synch with her song. She falls for him and the youthful penguins join in for singing and dancing to "Boogie Wonderland". The elders are appalled by Mumble's conduct, which they see as the reason for their lean fishing season. Memphis begs Mumble to stop dancing, for his own sake, but when Mumble refuses, he is exiled.
Mumble and the Amigos return to Lovelace, only to find him being choked by the plastic rings. Lovelace confesses they were snagged on him while swimming off the forbidden shores, beyond the land of the elephant seals. Not long into their journey, they are met by Gloria, who wishes to join with Mumble as his mate. Fearing for her safety, he ridicules Gloria, driving her away.
At the forbidden shore, the group finds a fishing boat. Mumble pursues it solo to the brink of exhaustion. He is eventually washed up on the shore of Australia, where he is rescued and kept at Marine World with Magellanic penguins. After a long and secluded confinement in addition to fruitlessly trying to communicate with the humans, he nearly succumbs to madness. When a girl attempts to interact with Mumble by tapping the glass, he starts dancing, which attracts a large crowd. He is released back into the wild, with a tracking device attached to his back. He returns to his colony and challenges the will of the elders. Memphis reconciles with him, just as a research team arrives, proving the claims of the existence of "aliens" to be true. The whole of the colony, even Noah the leader of the elders, engages in dance.
The research team returns their expedition footage, prompting a worldwide debate. The governments realize they are overfishing, leading to the banning of all Antarctic fishing. At this, the emperor penguins and the Amigos celebrate.

Question: What happens when a male song matches a female?
Answer: They mate.
Alternative answer: the male and female mate