dried flowerbud of a certain tropical tree, used as a spice, late 15c., earlier clowes (14c.), from Anglo-French clowes de gilofre (c. 1200), Old French clou de girofle "nail of gillyflower," so called from its shape, from Latin clavus "a nail" (from PIE root *klau- "hook"). For second element, see gillyflower. The two cloves were much confused in Middle English. The clove pink is so called from the scent of the flowers.
"slice or small bulb forming together a large bulb, as of garlic," Old English clufu "clove (of garlic), bulb, tuber," from Proto-Germanic *klubo "cleft, thing cloven" (source also of Old High German chlobo, Old Norse klofi), from PIE root *gleubh- "to tear apart, cleave."
Its Germanic cognates mostly lurk in compounds that translate as "clove-leek," such as Old Saxon clufloc, Old High German chlobilouh. Dissimilation produced Dutch knoflook, German Knoblauch.