From the Norman French form of the Germanic name Avelina, a diminutive of Avila. The Normans introduced this name to Britain. After the Middle Ages it became rare as an English name, though it persisted in America until the 19th century [1].
Possibly from the name of the prayer Ave Maria, in which Ave is Latin meaning “greetings, salutations”. In Estonian it is also associated with the word ava meaning “open”.