Fragment will generally refer to Gumball fragments. The term is also sometimes used to refer to Relics Fragment or (erroneously) to Airships chips.
Common sources for gumball fragments are areas like the Maze, Mercenary Camp or Events.
Common sources for airship chips are Sky exploration and the Alliance Shop.
30 fragments may be compressed into a Pearl. This is needed for the gumball trials and statues, also see: Fane Expansion