Do you have a friend who constantly turns the conversation to themselves, as in "That's great about your winning the award but do you think these pants look good on me?" They're putting their narcissism, or excessive love of self, on display.
In psychoanalysis, narcissism is erotic gratification derived from excessive love for yourself, and is considered to be a normal developmental stage. The reference is to Narcissus, a beautiful youth in Greek mythology who fell in love with his reflection in a body of water and was changed into the flower narcissus, which grows near water.