Hohenheim is many things. In the Anime he is a human who has been using the Philosopher Stone to jump from body to body for over 200 years in hopes to have immortality. Yet in the manga Hohenheim is a "monster" as he call himself, who has been living for hundreds of years traveling, trying to find a way to become mortal again so that he may live and die with his family.
He is also Ed and Al's father who walked out on them when they were only small children. Hohenheim realized that they hate him for it, and would never be a good father to them now, and that is his reason for not returning.
Hohenheim dies in the fullmetal Alchemist movie, when the city Ed and him are in fall under attack. He is then killed when their vehicle is hit, and flames ensue. Ed manages to escape.