To be pedantic, it's the first annual celebration of your birthday.
Other languages use a less confusing term for it: anniversaire (French) is just anniversary, verjaardag (Dutch) roughly means year-rollover-day, and cumpleaños (Spanish) signifies completion of another year.
I just realized something: anniversaire has the same root as the other examples I gave. It comes from the latin words annus and verso, which mean "year" and "to turn over" respectively.
late 14c., from Old English byrddæg, "anniversary or celebration of one's birth" (at first usually a king or saint); see birth (n.) + day. Meaning "day on which one is born" is from 1570s. Birthnight is attested from 1620s.
https://www.etymonline.com/word/birthday#etymonline_v_27158
