The Holy Crown of Hungary was given to St. Stephen, the first Christian king of Hungary, in 1001 AD. The Hungarians sent a delegation to Rome to recieve a crown and be officially recognized as a Christian state by the Church; when they arrived, they realized that the proper procedure was to petition first, to allow time for the crown to be made and other arrangements to be readied. Not wanting to wait, and seeing that a crown was ready for a Polish delegation that was running late, the Hungarians passed themselves off as Poles and took the crown back to Hungary.
St. Stephen was crowned in the Coronation Basilica in Esztergom, whereupon he offered the crown, the authority, the land and the nation into the care of the Virgin Mary. The Crown, therefore, is the true ruler in Hungary; he who wears it simply makes the decisions. Because the crown is the symbol of the Virgin's authority, it is also revered and adored by Roman Catholics.
The crown that was given to St. Stephen was actually only the round, bottom portion of the modern crown. The domed top half was given to St. László, three hundred years later. As to why the cross on the top is bent, there is no reliable explanation. Most probably, it was damaged in one of the many hasty evacuations that occured when some barbaric nation or another occupied the palace. Nonetheless, it has never been straightened, and even appears so on the Coat of Arms.