This name was very popular in the English-speaking world at the end of the 19th century. Though it declined in use over the next 100 years, it staged a successful comeback at the end of the 20th century. The American sitcom Will and Grace (1998-2006) may have helped, though the name was already strongly rising when it premiered. It was the top name for girls in England and Wales in 2006.
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.