c.1500, from Middle English ampte (late 14c.), from Old English æmette "ant," from West Germanic *amaitjo (cf. Old High German ameiza, German Ameise) from a compound of bases *ai- "off, away" + *mai- "cut," from PIE *mai- "to cut" (cf. maim). Thus the insect's name is, etymologically, "the biter off."
Emmet survived into 20c. as an alternative form. White ant "termite" is from 1729. To have ants in one's pants "be nervous and fidgety" is from 1934, made current by a popular song; antsy embodies the same notion.