The noun is derived from cat + head.
Sense 1.1 (“heavy piece of timber projecting from a ship on which an anchor is raised or lowered, and secured”) is from the fact that such a timber traditionally had a cat or lion’s head carved on its end. Sense 4 (“ellipsis of cathead biscuit”) is apparently from the fact that the biscuit is similar in size to a cat’s head.
The verb is derived from the noun.