The first part of the "secret" of Fatima was a vision of hell, the second part was a warning of a future war. The second part is believed to have been a prediction of WW2. The third part according to the Congregation for the Doctrine of the Faith was:
we saw an Angel with a flaming sword in his left hand; flashing, it gave out flames that looked as though they would set the world on fire; but they died out in contact with the splendour that Our Lady radiated towards him from her right hand: pointing to the earth with his right hand, the Angel cried out in a loud voice: 'Penance, Penance, Penance!'. And we saw in an immense light that is God: something similar to how people appear in a mirror when they pass in front of it' a Bishop dressed in White we had the impression that it was the Holy Father'. Other Bishops, Priests, men and women Religious going up a steep mountain, at the top of which there was a big Cross of rough-hewn trunks as of a cork-tree with the bark; before reaching there the Holy Father passed through a big city half in ruins and half trembling with halting step, afflicted with pain and sorrow, he prayed for the souls of the corpses he met on his way; having reached the top of the mountain, on his knees at the foot of the big Cross he was killed by a group of soldiers who fired bullets and arrows at him, and in the same way there died one after another the other Bishops, Priests, men and women Religious, and various lay people of different ranks and positions. Beneath the two arms of the Cross there were two Angels each with a crystal aspersorium in his hand, in which they gathered up the blood of the Martyrs and with it sprinkled the souls that were making their way to God.
The Church has understood the third secret to refer to atheistic communism's attacks on the Church and that the bishop dressed in white refers to the attempted assassination of Blessed Pope John Paul II.
As the Congregation for the Doctrine of the Faith noted:
A careful reading of the text of the so-called third "secret" of Fatima, published here in its entirety long after the fact and by decision of the Holy Father, will probably prove disappointing or surprising after all the speculation it has stirred. No great mystery is revealed; nor is the future unveiled...
...That here 'a mother's hand' had deflected the fateful bullet only shows once more that there is no immutable destiny, that faith and prayer are forces which can influence history and that in the end prayer is more powerful than bullets and faith more powerful than armies.
So not only does the secret of Fatima not refer to the end of the world in December 2012, it does not refer to the end of the world at all.