Known bearers of this name include a daughter of the American mathematician and religious leader Orson Pratt (1811-1881) and the American abolitionist and philanthropist Laura Spelman Rockefeller (1839-1915), who carried the name as a middle name and was affectionately referred to as Cettie because of it.
In popular culture, this name is best known for being the name of princess Celestia, who is a character in the animated children's television series "My Little Pony: Friendship is Magic".
As an English name it has been in use since the Middle Ages, originally in the form Clare, though the Latinate spelling Clara overtook it in the 19th century and became very popular. It declined through most of the 20th century (being eclipsed by the French form Claire in English-speaking countries), though it has since recovered somewhat.
There was a medieval English form of this name, Helewis, though it died out after the 13th century. In the 19th century it was revived in the English-speaking world in the form Eloise.