"small, hanging piece from a garment," c. 1400, of uncertain origin but probably from a Scandinavian source (compare Norwegian tagg "point, prong, barb," Swedish tagg "prickle, thorn") and related to Middle Low German tagge "branch, twig, spike"), from Proto-Germanic *tag-. The sense development might be "point of metal at the end of a cord, string, etc.," hence "part hanging loose." Or perhaps ultimately from PIE *dek-, a root forming words referring to "fringe; horsetail; locks of hair" (see tail (n.1)).
Meaning "a label" is first recorded 1835; sense of "automobile license-plate" is recorded from 1935, originally underworld slang. Meaning "an epithet, popular designation" is recorded from 1961, hence slang verb meaning "write graffiti in public places" (1990).
It forms all or part of: attain; contact; contaminate; entire; intact; integer; integrate; integrity; noli me tangere; tact; tactics; tactile; tangent; tangible; task; taste; tax; taxis.
It is the hypothetical source of/evidence for its existence is provided by: Latin tangere "to touch," taxare "to touch, assess," tactus "touch," integer "intact, whole, complete, perfect; honest;" Greek tassein "to arrange," tetagon "having seized;" Old English þaccian "stroke, strike gently."