The characters were originally low-life criminals from the planet Ghennix. When Ghennix was destroyed by Unicron, the criminals attempted to escape in a small spaceship, but Unicron caught them very easily.
Instead of killing the criminals, Unicron reformatted them into three powerful assassins, whom he named Hook, Line, and Sinker. Each was given new weapons: Hook (not to be confused with the Constructicon member Hook) has a hook on one of his hands and a harpoon on the other, Line carries a sword and a net, and Sinker has two massive steel balls at the end of his arms.
Hook, Line, and Sinker's first mission was to fetch Galvatron from an alternate timeline. In this timeline, the Decepticons had won against the Autobots in 2009. Galvatron was leading the Pretender Monsters onto a final victory march into New York City, when Hook, Line, and Sinker captured him and brought him to the "real" timeline, into the 1980s.
Unicron intended Galvatron to serve as his chief assassin and Hook, Line, and Sinker to serve as Galvatron's assistant assassins. However, when Galvatron met Emirate Xaaron deep under the surface of Cybertron, he rebelled against Unicron and (at least apparently) sided with Xaaron instead. Through a psychic link, Unicron was immediately aware of this treachery, and sent Hook, Line, and Sinker to kill Galvatron. They failed, as Galvatron killed them instead.
Hook is also the name of one of the Constructicons. Line and Sinker, however, are unique names in the entire Transformers universe.