late 14c., mesche, "open space in a net," probably from late Old English max "net," earlier mæscre, from Proto-Germanic *mask- (cf. Old Norse möskvi, Danish maske, Swedish maska, Old Saxon masca, Middle Dutch maessce, Dutch maas "mesh," Old High German masca, German Masche "mesh"), from PIE root *mezg- "to knit, plait, twist" (cf. Lithuanian mezgu "to knit," mazgas "knot").
1530s, originally in the figurative sense of "entangle, involve," from mesh (n.). Literal sense "to become enmeshed" is from 1580s. Meaning "to fit in, combine" is from 1944. Related: Meshed; meshing.