noun
birthday celebration
Refers to the act of celebrating a birthday, or a gift/party for that purpose.
友達の誕生祝いにケーキを買った。
I bought a cake for my friend's birthday celebration.
誕生日 is 'birthday' (the date), while 誕生祝い is the celebration or gift for that day.
Compound of 誕生 (birth) and 祝い (celebration).