Half-Elven

The Half-elven or Peredhil were people of Middle-earth, the name of whom was primarily applied to Elrond and Elros in the Second and Third Age, but also to Eärendil and his wife Elwing before them. They were called so because of their mixed Edain (Human) and Eldarin (Elven) blood
At the end of the First Age, they were given a choice to be Elven and immortal, or to be of the race of Men and accept the Gift of Men which is death.
Others considered Half-elven were Elrond's children Elladan, Elrohir, and Arwen. They, like the other Half-elven before them, were given the choice of mortality.