What does Boxing Day have to do with boxing?
1630s, "incapable of being touched," from French intangible (c.1500) or directly from Medieval Latin intangibilis, from in- "not" (see in- (1)) + Late Latin tangibilis "that may be touched" (see tangible). Figurative sense of "that cannot be grasped by the mind" is from 1880. Noun meaning "anything intangible" is from 1914. Related: Intangibly.