1. A date that is observed on an annual basis because it is the same date as an important event in a past year; such as, the date of someone's wedding.
2. A celebration or other commemorative ritual marking the date of an important event.
3. Etymology: from Latin anniversarius, "returning annually", from annus, "year" + versus; past participle of vertere. "to turn". The adjective came to be used as a noun in Church Latin as anniversaria dies with reference to saints' days.

The year rolls around to bring the anniversary of birth, marriage, or some other event; and this "turning" of the year is the literal meaning of the word anniversary.