Half-Elves are the products of a union between an Elf and a Human. Why Humans and Elves can interbreed is a matter than neither Alchemist nor Clergyman has resolved, but it is known that while a human-elf pairing always produces a half-elf, that other pairings are less specific. Human/Half-Elf pairings tend to produce humans, but that is not universally true, and sometimes elven features can crop up in a family several generations later. Elf/Half-Elf pairings always produce another half-elf.
Half-Elves are a part of two worlds, but belong in neither, and for this their lives are often troubled. Typically they will live in the community of their mothers. Those born to human mothers have to live with distrust on a part of their peers and communities. Seen as a sign of immorality or wickedness, even those who grow up with the trust of their community must contend with the scorn of the greater world. Because of this many end up travelers, mirroring their nomadic fore-fathers, or find positions on the edges of society. Those born to elven mothers fair perhaps better, for while their community likewise views them as partially outsiders, it tends to be more forgiving… if a tad paternalistic. To elves, Half-elves are signs of dalliance or reminders of their societies decline. They are short-lived, and all elves pity knowing that the young child they see now will be an old man while they are still young.
There are rare instances of Half-elves who grow up with both parents, usually in one of the larger cities with an Elven community, and they may have it easier, but still, they will live as outsiders apart from the world.
Half-Elves use the standard information for Half-Elves in the Pathfinder RPG.