Definition: to fail; to flop.

Origin
Just looking at an egg should give you a clue as to how this came about. The original phrase — goose-egg — was used in the sporting world and referred to a score of zero. At some point the phrase was shortened to just egg and extended beyond sports usage to encompass any unsuccessful act which makes you look like a real zero.

Answers Swan Song Albatross around your neck To curry favor Neither fish nor fowl To lay an egg