This was the name of the first English baby born in the New World: Virginia Dare in 1587 on Roanoke Island. Perhaps because of this, the name has generally been more popular in America than elsewhere in the English-speaking world, though in both Britain and America it was not often used until the 19th century. The baby was named after the Colony of Virginia, which was itself named for Elizabeth I, the Virgin Queen. A more recent bearer was the English novelist Virginia Woolf (1882-1941).
It has occasionally been used as an English given name since the 16th century. It was moderately popular in the 1940s, but had a more notable upswing in the early 2000s. This may have been inspired by the Spanish actress Penélope Cruz (1974-), who gained prominence in English-language movies at that time. It was already rapidly rising when celebrities Kourtney Kardashian and Scott Disick gave it to their baby daughter in 2012.
In the English-speaking world this name has been occasionally given since the early 20th century. It started rising in America after the variant Lorelai was used for the main character (and her daughter, nicknamed Rory) on the television series Gilmore Girls (2000-2007).
As a rarer (but older) masculine name it is probably derived from a surname: see Fay 1 or Fay 2.