Prior to the wedding of William and Kate, this tiara was commonly known as the Scroll Tiara. In the official information released about the bride's attire, the Palace referred to it as a 'halo' tiara, so I'll go with: the Halo Scroll Tiara. This delicate diamond piece has served as something of a starter tiara for royal ladies throughout the years, beginning with Queen Elizabeth the Queen Mother.
The tiara was made by Cartier in 1936 and was purchased by the Duke of York for his Duchess three weeks before he became King George VI, and she became Queen Elizabeth (the future Queen Mother). The only picture of her wearing it was taken after she received it and before she became Queen Consort. Apparently it wasn't a favorite, as she switched to other, grander pieces once her tiara access increased.
She soon passed the tiara on to her daughter, Princess Elizabeth (the current Queen), as an 18th birthday present (1944). This Queen must not have been terribly fond of it either, as she's never worn it publicly.
The Queen has made a practice of lending it out, however. The first loan was to Princess Margaret, and it became a go-to tiara in her early years. She stopped wearing it as her own tiara collection grew, especially after the Queen Mother gave Margaret the papyrus or lotus flower tiara.
And it served the very same purpose for Princess Anne, who also borrowed this tiara. She last wore the Halo Scroll Tiara publicly in the early 1970s, at which point the Queen had given her the Meander Tiara and she had received the Festoon Tiara as a gift for a ship christening.
After a few decades' rest, the tiara made its most famous appearance to date: anchoring the bridal veil of Catherine Middleton.
And as a bonus for the new Duchess, she already has matching earrings: a gift from her parents for her wedding day, these specially commissioned pieces from Robinson Pelham perfectly echo the scroll elements in addition to including acorns to echo her family's crest.