Debrett's page on white tie has more details about tiara etiquette:
Jewellery can be striking; this is the time for the finest jewels and gems, including tiaras. Traditionally these are worn for the first time by brides, and subsequently by married women only. It is incorrect for young girls to wear tiaras on any occasion.
Some years ago the V&A had a tiara exhibition. I remember they said that tiaras first came into fashion in the early 19th century as part of the French Empire/Regency trend for reviving ancient Roman costume. As they are worn for the first time by brides, they would sometimes be bought/remodelled as wedding presents (as happened with Sarah Ferguson and Sophie Wessex), and could be part of a parure. They're a status symbol - e.g. Princess Diana, being an aristocrat, had a family tiara to wear, but other royal brides did not.