Short answers, pulled from the story.
Skaði is a jötunn and goddess associated with bowhunting, skiing, winter, and mountains. She is the daughter of the jötunn Þjazi and appears in the Poetic Edda, the Prose Edda, and Heimskringla. She is also called Öndurguð, meaning "ski god," and Öndurdís.
Skaði traveled to Asgard armed with a helmet, a coat of mail, and all weapons of war to demand compensation for the killing of her father Þjazi. The gods agreed to let her choose a husband by looking only at their feet, and Odin made two stars from Þjazi's eyes as part of the settlement.
Skaði chose her husband by looking only at the feet of the assembled gods. Believing the most attractive feet belonged to Baldr, she declared "I choose that one; there can be little that is ugly about Baldr," but the feet turned out to belong to Njörðr.
Skaði and Njörðr could not agree on where to live. Njörðr found Skaði's mountain home of Þrymheimr hateful after nine nights, missing swans and disliking the howling of wolves, while Skaði could not sleep at his sea-side home of Nóatún because a gull woke her each morning. She eventually returned permanently to Þrymheimr.
After the gods bound Loki with the entrails of his son Nari, Skaði fastened a venomous serpent above his face so that venom would drip onto him. The Prose Edda states that Loki's writhing in pain from the venom is the source of earthquakes.
The etymology of Skaði is uncertain. Scholar John McKinnell connects it to Germanic words meaning "shadow," such as Gothic skadus and Old English sceadu, and suggests a possible link to the name Scandinavia. Georges Dumézil argued the opposite: that Skaði's name derived from the geographical region rather than giving the region its name.