What is the diadem in Harry Potter and the Deathly Hallows?

A diadem is a jeweled crown worn as a symbol of sovereignty. The diadem in the Harry Potter books is Rowena Ravenclaw's and it was believed that it bestowed apon the wearer incredible wit. It was stolen by her daughter a long time ago and was lost. This is why the diadem is refered to as "the lost diadem of Ravenclaw"

In the last part of the book, Harry and his friends believe it is a horcrux and contains a piece of Lord Voldemorts soul. Voldemort cannot die without all the horcruxes being destroyed so therefore, Harry needs to destroy the diadem. The only problem is that it is lost.