• 誕生たんじょう — birth
• 誕生日たんじょうび — birthday
• 生誕せいたん — (commemorative / formal) birth

誕 combines 言 (words/speech) and 延 (extend). It originally described words about someone’s coming into being, and came to mean “birth” in ceremonial or formal contexts.

It’s a 5th-grade 教育漢字, often seen in 誕生 and 誕生日.