Originating in the sport of boxing this phrase has to do with the countdown a ref gives when one of the boxers hits the floor and can't get back up. In a figurative sense it refers to someone being unable to complete something and is defeated. 

'Don't count your chickens' is one of the oldest, and possibly the wisest. The thought was recorded in print by Thomas Howell in New Sonnets and pretty Pamphlets, 1570: Counte not thy Chickens that vnhatched be, Waye wordes as winde, till thou finde certaintee Samuel Butler continued the pleasing rhyming in his expression of the proverbial advice, in the narrative poem Hudibras, 1664: To swallow gudgeons ere they're catch'd, And count their chickens ere they're hatched. ( source ) Using it today we mean that until something is final or actually happens as predicted we shouldn't count on it.