* Fleamont Potter was a wealthy wizard who invented the famous "Sleekeazy's Hair Potion", which made him very rich. He was also a pure-blood wizard who disliked Muggle-borns, a prejudice that his son, James, did not inherit. Fleamont died of a mysterious illness shortly before Harry was born.
* Euphemia Potter was a kind and loving woman who was a good witch, but not particularly talented. She was a devoted mother and grandmother. She died from a mysterious illness shortly after Fleamont.
The mysterious illness that killed both Fleamont and Euphemia Potter is strongly implied to be a curse placed by Voldemort, who was already targeting Harry's family. This is never explicitly stated, but it fits with Voldemort's known modus operandi and his desire to eliminate any threat to him.
Harry's paternal grandparents are not mentioned in the books.