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.

its the same in English:

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