The meaning of Avani is  Earth . Its origin is  Sanskrit . This name is mostly being used as a girls name. Last year it ranked 1,497th in the U.S. Social Security Administration list of most popular baby girl names.Avani means earth in Sanskrit.his name is mostly being used as a girls name. Last year it ranked 1,497th in the U.S. Social Security Administration list of most popular baby girl names. Avani means earth in Sanskrit.