A hagiography is a type of biography that puts the subject in a very flattering light. Hagiographies are often about saints.
The two halves of hagiography refer to holiness and writing, and it is something written about holy people. Originally, a hagiography was a biography of a saint written without skepticism or criticism. A hagiography idealizes the subject and puts them on a pedestal. These days, a hagiography is not necessarily written about a saint, but it still idolizes the subject. A hagiography makes the subject seems like a hero, or at least a wonderful, nearly perfect person.