c.1400, from O.N.
grod "pit," or M.Du.
groeve "furrow, ditch," from P.Gmc.
*grobo (cf. O.N.
grof "brook, river bed," O.H.G.
gruoba "ditch," Goth.
groba "pit, cave," O.E.
græf "ditch"), related to
grave (n.). Sense of "long, narrow channel or furrow" is 1659. Meaning "spiral cut in a phonograph record" is from 1902. Fig. sense of "routine" is from 1842, often depreciatory at first, "a rut." Adj.
groovy is 1853 in lit. sense of "of a groove;" 1937 in slang sense of "excellent," from jazz slang phrase
in the groove (1932) "performing well (without grandstanding)." As teen slang for "wonderful," it dates from 1944; popularized 1960s, out of currency by 1980.
[groov] 
noun, verb, grooved, groov⋅ing.