c. 1200, "to take, capture," from Anglo-French or Old North French cachier "catch, capture" (animals) (Old French chacier "hunt, pursue, drive (animals)," Modern French chasser "to hunt;" making it a doublet of chase (v.)), from Vulgar Latin *captiare "try to seize, chase" (also source of Spanish cazar, Italian cacciare), from Latin captare "to take, hold," frequentative of capere "to take, hold," from PIE root *kap- "to grasp."
Its senses in early Middle English also included "chase, hunt," which later went with chase (v.). Of sleep, etc., from early 14c.; of infections from 1540s; of fire from 1734 (compare Greek apto "fasten, grasp, touch," also "light, kindle, set on fire, catch on fire"). Related: Catched (obsolete); catching; caught.
Meaning "act as a catcher in baseball" recorded from 1865. To catch on "apprehend, understand" is 1884, American English colloquial. To catch the eye "draw the attention" is attested by 1718. Catch as catch can has roots in late 14c. (cacche who that cacche might).