late 14c., "middle point of a circle; point round which something revolves," from Old French centre (14c.), from Latin centrum "center," originally the fixed point of the two points of a drafting compass (hence "the center of a circle"), from Greek kentron "sharp point, goad, sting of a wasp," from kentein "stitch," from PIE root *kent- "to prick" (source also of Breton kentr "a spur," Welsh cethr "nail," Old High German hantag "sharp, pointed").
The spelling with -re was popularized in Britain by Johnson's dictionary (following Bailey's), though -er is older and was used by Shakespeare, Milton, and Pope. Meaning "the middle of anything" attested from 1590s. Figuratively, "point of concentration" (of power, etc.) is from 1680s. Political use, originally in reference to France, "representatives of moderate views" (between left and right) is from 1837. Center of gravity is recorded from 1650s. Center of attention is from 1868.