In some cases this name can be a short form of longer names that start with Leo, such as Leonard.
This is the usual form of the name Elizabeth in Spain and Portugal, though elsewhere it is considered a parallel name, such as in France where it is used alongside Élisabeth. The name was borne by two Spanish ruling queens, including Isabel of Castile, who sponsored the explorations of Christopher Columbus.
This is also an alternate transcription of Russian Ева (see Yeva).
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.