late Old English tannian "to convert hide into leather" (by steeping it in tannin), from Medieval Latin tannare "tan, dye, a tawny color" (c.900), from tannum "crushed oak bark," used in tanning leather, probably from a Celtic source (e.g. Breton tann "oak tree"). The meaning "make brown by exposure to the sun" first recorded 1520s. To tan (someone's) hide in the figurative sense is from 1660s. Related: Tanned; tanning.
"bronze color imparted to skin by exposure to sun," 1749, see tan (v.). As a simple name for a brownish color, in any context, it is recorded from 1888. The adjective tan "of the color of tanned leather" is recorded from 1660s.
Abbreviation of tangent
To beat someone severely; thrash: Fetch me my gin, son, 'fore I tan your hide
[1670+; fr the making of a hide into leather by tanning]