Short answers, pulled from the story.
Líf and Lífþrasir are two humans foretold to survive Ragnarök, the Norse end of the world. They shelter in a place called Hoddmímis holt, eating morning dew, and emerge afterward to repopulate a newly risen and fertile world. All future generations are said to descend from them.
Líf is identical with the Old Norse noun for life, specifically the life of the body. Lífþrasir is a masculine name formed from líf and the element þrasir; the medieval Lexicon Poëticum defines it as 'Líf's lover, lover of life, zest for life.'
Líf and Lífþrasir appear in the Poetic Edda, compiled in the 13th century from earlier traditional sources, and in the Prose Edda, written in the 13th century by Snorri Sturluson. The poem Vafþrúðnismál and chapter 53 of Gylfaginning both record their story.
Hoddmímis holt is the wood where Líf and Lífþrasir shelter during Ragnarök. Scholars Carolyne Larrington and Rudolf Simek both argue it is not a literal forest but an alternative name for Yggdrasil, the world-tree, based on a connection between the figures of Mímir and Yggdrasil in earlier Norse poetry.
Fimbulvetr is the catastrophic winter that precedes the end of the world in Norse mythology. In the poem Vafþrúðnismál, Odin asks the jötunn Vafþrúðnir who among humanity will survive Fimbulvetr, and Vafþrúðnir answers that it will be Líf and Lífþrasir.
Rudolf Simek argues that Líf and Lífþrasir sheltering inside a tree repeats the original creation of humanity. Askr and Embla, the first humans in Norse mythology, were created from tree trunks, so placing the surviving pair inside a tree at the world's end doubles that first act of creation.