early 13c., "small door or gate," especially one forming part of a larger one, from Anglo-French wiket, Old North French wiket (Old French guichet, Norman viquet) "small door, wicket, wicket gate," probably from Proto-Germanic *wik- (source also of Old Norse vik "nook," Old English wican "to give way, yield"), from PIE root *weik- (2) "to bend, to wind." The notion is of "something that turns." Cricket sense of "set of three sticks defended by the batsman" is recorded from 1733; hence many figurative phrases in British English.
An observant sailor watching a strange vessel approach at sea judges her character by the condition of the jibs; hence cut of (one's) jib "personal appearance" (1821). Related: Jib-boom (1748). The jib in jib-door "door flush with a wall" (1792) is of uncertain origin and probably is not the same word.
"coffee-room, viewed from the inside through a glass door, as it was seen by Dickens on a dark London day; ... used by Chesterton to denote the queerness of things that have become trite, when they are seen suddenly from a new angle." [J.R.R. Tolkien, "On Fairy Stories"]