In the United States it became more common for girls in the early 1980s, shortly after the debut of the television sitcom The Facts of Life (1979-1988), which featured a character named Blair Warner. The name left the American top 1000 rankings two decades later, but was resurrected by another television character, this time Blair Waldorf from the series Gossip Girl (2007-2012).
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.
Originally more common as a name for boys in America, it became more popular for girls in the 1960s. It began rapidly increasing after 1973, possibly due to a character (played by Natalie Wood) in the television movie The Affair. It reached an apex in the United States ranked 17th in 1990, though it has quickly fallen away since then.
This name was common among continental European royalty during the Middle Ages, and it was popularized in Britain by the German House of Hanover when they inherited the British throne in the 18th century. It was the name of characters in the novels Tom Jones (1749) by Henry Fielding and The Vicar of Wakefield (1766) by Oliver Goldsmith.
In the United States this name was only moderately common until the 1990s when it began rising in popularity, eventually becoming the most popular for girls from 2011 to 2013. A famous bearer is the Italian actress Sophia Loren (1934-).