the anniversary of the day on which a person was born, typically treated as an occasion for celebration and the giving of gifts:his twenty-ninth birthday [as modifier]:a birthday cake
the day of a person’s birth:he shares a birthday with Rod Stewart
the anniversary of something’s origin or foundation:the seventy-fifth birthday of the Institute
Phrases
in one's birthday suit
humorous naked.
birthday in other Oxford dictionaries
Definition of birthday in the US English dictionary