"Can I bring a friend to your birthday party?" "Of course! The more people we have, the more fun it will be."
Remember how 誕生 is birth? If you add day on there, you have a birthday. Happy birthday!
This is a jukugo word, which usually means on'yomi readings from the kanji, but with this word 日 uses the kun'yomi ひ, which is turned into び due to rendaku.