Every great chef has a defining recipe -- A signature dish is that recipe that identifies an individual chef. It should be unique and allow an informed gastronome to name the chef. It can be thought of as the culinary equivalent of an artist finding their own style, or an author finding their own voice. A chef's signature dish often changes with time or they may claim several signature dishes.
A signature dish can also be used to refer to a culinary region, in which case its meaning may be the equivalent of "national dish".