The Laestrygonians, mythologically speaking, are a race of giant cannibals. In the Odyssey, they live in the city of Telepylus on an island that appears to be roughly shaped like a horseshoe (or at least one part of it is.) Their ruler is Antiphates.
All the other ships with Odysseus sail into the harbor (the open part of the horseshoe which is surrounded by cliffs) where the water is calmer. Odysseus keeps his ship outside of the harbor moored to a rock.
Odysseus sends a couple of his men to check out the island (he can't see much from way outside the harbor) and his men come across a woman who says she is the daughter of the king. The woman invites them home. Upon arriving, they see the woman's mother, a giant, who yells for her husband. The husband, the king Antiphates, appears, grabs one of the crew, and starts chomping on him.
The others manage to make a run for it, but Antiphates whoops it up to his fellow cannibals and the ships in the harbor are all ambushed. The giants chuck rocks down at them and spear the sailors like shish-kabob. Only Odysseus, who has kept his ship out of the harbor, manages to survive with his crew.