1680s, originally "to seize with the pounces," from Middle English pownse (n.) "hawk's claw" (see pounce (n.)). Meaning "to jump or fall upon suddenly" is from 1812. Figurative sense of "lay hold of eagerly" is from 1840. Related: Pounced; pouncing.
"claw of a bird of prey," late 15c., pownse, probably from Old French ponchon "lance, javelin; spine, quill" (Modern French poinçon; see punch (v.)). So called for being the "claws that punch" holes in things. In falconry, the heel claw is a talon, and others are pounces. Meaning "an act of jumping or falling upon" is from 1825. In Middle English also the name of a tool for punching holes or embossing metal (late 14c.).