“Yeah, but the lost diadem is lost, Luna. That’s sort of the point.”
-- Michael Corner to Luna Lovegood (DH29)
A diadem (also called a tiara) that bestows wisdom on the wearer. It is etched with the words, “Wit beyond measure is man’s greatest treasure” (DH29, DH31). The diadem was stolen by Helena Ravenclaw in an effort to surpass her mother Rowena Ravenclaw. Helena Ravenclaw then fled to Albania, where the diadem remained hidden in a hollow tree for centuries after her death, until Tom Riddle managed to charm her ghost into revealing its whereabouts (DH31).
Dumbledore has told Harry that there is something of Ravenclaw's that Voldemort may have turned into a Horcrux.
“Yes,” said Dumbledore, smiling, “I would be prepared to bet — perhaps not my other hand — but a couple of fingers, that they became Horcruxes three and four. The remaining two, assuming again that he created a total of six, are more of a problem, but I will hazard a guess that, having secured objects from Hufflepuff and Slytherin, he set out to track down objects owned by Gryffindor or Ravenclaw. Four objects from the four founders would, I am sure, have exerted a powerful pull over Voldemort’s imagination. I cannot answer for whether he ever managed to find anything of Ravenclaw’s." (HBP23) This is revealed to be the Diadem of Ravenclaw in Deathly Hallows.
Xenophilius Lovegood tried to recreate it, but with, um, mixed results (DH20).
Vincent Crabbe destroys the diadem of Ravenclaw with Fiendfyre:
“He pulled the diadem from his wrist and held it up. It was still hot, blackened with soot, but as he looked at it closely he was just able to make out the tiny words etched upon it: WIT BEYOND MEASURE IS MAN’S GREATEST TREASURE.
A bloodlike substance, dark and tarry, seemed to be leaking from the diadem. Suddenly Harry felt the thing vibrate violently, then break apart in his hands, and as it did so, he thought he heard the faintest, most distant scream of pain, echoing not from the grounds or the castle, but from the thing that had just fragmented in his fingers." (DH31)
The diadem of Ravenclaw is one of four Hogwarts relics from the Founders related to Voldemort's Horcruxes. The others are Helga Hufflepuff's Cup, Salazar Slytherin's Locket, and the sword of Gryffindor.
"Diadem" is an Old French term, "diademe," which is directly from Latin, "diadema," meaning "cloth band worn around the head as a sign of royalty."