Is a tiara(or diadem) that belonged to Rowena Ravenclaw. It is supposed to give the wearer infinite wisdom. Rowena's daughter--who is now the ghost of the Grey Lady stole the diadem from her mother and hid it in a forest in Albania. She told no one else this story except for Tom Riddle and then, years later, Harry Potter.
It is important to the series because Voldemort turns the diadem into one of the Horcruxes. It was hidden in the Room of Requirement.
Harry actually sees it in "Half-Blood Prince" when he places it on the head of the bust of an ugly warlock in order to mark the cabinet holding his Potions book. It is then destroyed in "Deathly Hallows" when Crabbe unwittingly uses the Fiendfyre (cursed fire) spell--thus destroying the Horcrux as well. THis does not happen in the movies though.
What happens in the film is that they escape the fiendfyre with the diadem. Ron tosses Harry a basilisk fang to kill the Horcrux. Then Ron kicks it into the fiendfyre just before the door to the room slams shut. Harry senses the Horcruxes in the film version as his way to find them and to feel the pain when they are destroyed. It's a good alterate ending.