Hagrid’s father was a wizard who had a child, Rubeus Hagrid, with a giantess named Fridwulfa. After Fridwulfa abandoned her family when Rubeus was very young, Mr. Hagrid raised his half-giant son as a single father. He died while Rubeus was a second-year at Hogwarts (GF23).
Other canon notes and references
Rubeus Hagrid's worst fear/memory was his father's death (PA11).