I believe The Red Comet is what is mentioned in the prophecy of Azor Ahai
There will come a day after a long summer when the stars bleed and the cold breath of darkness falls heavy on the world. In this dread hour a warrior shall draw from the fire a burning sword. And that sword shall be Lightbringer, the Red Sword of Heroes, and he who clasps it shall be Azor Ahai come again, and the darkness shall flee before him.
The red comet -- or the bleeding star, if you will -- is the fulfilment of part of that prophecy, and it appears when Dany hatches her dragon eggs in Drogo's funeral pyre.
There are many theories and much speculation on this, and it is also related to the Prince that was promised, something that Rhaegar Targaryen was preoccupied with investigating.
It is also said
When the red star bleeds and the darkness gathers, Azor Ahai shall be born again amidst smoke and salt to wake dragons out of stone.
We can note that Daenerys has done all of these things. Her final sacrifice is also mirrored in the story of Nissa Nissa, the wife of Azor Ahai, who had to be sacrificed to make the legendary sword Lightbringer. (Yes, Melisandre tried to create a magic sword for Stannis, which she claimed was Lightbringer) Daenerys burned her husband Drogo, and Mirri Maaz Duur.
She woke the dragons from stone eggs. She was reborn in the fire (smoke). Lightbringer is her dragons.
Oh, and also, (Spoiler AFFC)
Maester Aemon became convinced of this after meeting Xhondo:
Daenerys is the one, born amidst salt and smoke. The dragons prove it.
Xhondo's captain is Quhuru Mo, who met Daenerys and her dragons in Qarth (A Clash of Kings)