Van Hohenheim is Edward and Alphonse Elric's father—and a genuinely brilliant alchemist in his own right. He's best known for abandoning his family when Al was still an infant and Ed was barely old enough to remember him. Their mother, Trisha, raised the boys alone until her death, an event Ed has always blamed on their father's absence. Even years later, Ed can't let go of that resentment.
Interestingly, his actual name is Van Hohenheim, not Hohenheim Elric. Ed himself makes this point clear in the manga, noting that "Elric" is their mother's surname—so the family name comes through her side.
The character's portrayal shifts notably between versions of the story. His role and backstory differ between the 2003 anime adaptation and the manga/2009 anime continuity, which took the story in separate directions.
Content compiled by AnimeList.moe from publicly available sources.