The prince that was promised
From A Wiki of Ice and Fire
The prince that was promised is a prophesied leader or saviour. The prince may be part of an ancient prophecy, a prophecy that foretells the coming of a hero to deliver the world from darkness. A "bleeding star" is supposed to herald the coming of the prince. The prince is said to have "a song" - the song of ice and fire.
At the moment it is not known exactly where the prophecy originates, information on the prince that was promised is rather scant. Based on the fact that Maester Aemon mentions “a thousand years”  to Samwell Tarly it should be safe to say the prince that was promised prophecy is at least 1,000 years old. According to Melisandre the prince that was promised coming was prophesied 5,000 years ago.  She does not mention who made the prophecy.
Melisandre has mentioned the prince that was promised  and Azor Ahai interchangeably but she tends to use the name Azor Ahai far more often. Maester Aemon only ever mentioned the prince that was promised, never the name Azor Ahai.
It appears as if the Targaryen family had been awaiting the arrival of the prince so the prophecy may come from Old Valyria - but that is conjecture. There is not as much clear information on the prince as, for example, Azor Ahai.
Thus far there has been no mention of the prince wielding a sword - unlike the last hero and Azor Ahai. However at one point Prince Rhaegar Targaryen believed that he might be the prince that was promised. According to a tale told of Rhaegar one day he found something in his scrolls that changed him and he decided to become a knight. He said to Ser Willem Darry, the master-at-arms,
|“||I will require a sword and armor. It seems I must be a warrior.||”|
Therefore, the prince may be a warrior who wields a sword.
|“||“He is the prince that was promised, and his is the song of ice and fire.||”|
|“||“When the red star bleeds and the darkness gathers, Azor Ahai shall be born again amidst smoke and salt.||”|
Much later in Braavos, when talking of the prince to Samwell Tarly Maester Aemon mentions smoke and salt as being part of the heralding of the prince that was promised coming. Obviously the mention of smoke and salt immediately brings to mind Melisandre’s above mentioned statement. However it is important to keep in mind what Tyrion Lannister has stated about prophecy,
|“||“Prophecy is like a half-trained mule. It looks as though it might be useful, but the moment you trust in it, it kicks you in the head." ||”|
Therefore, readers have to be careful of being kicked in the head by smoke and salt also being mentioned in relation to the prince that was promised. Azor Ahai and the prince that was promised may be two distinct prophecies, or they may be one in the same in a prophecy that has the potential to turn out to be about two separate people. It is easy get rather confused. Indeed the prince may not even be male; the prince may have been referred to as male erroneously for centuries. Before his death Maester Aemon came to firmly believe that the prince is not a prince but a princess.
Maester Aemon also says to Samwell that the dragon must have three heads. He wakes up weeping, wailing:
|“||The dragon must have three heads…but I am too old to be one of them. I should be with her, showing her the way, but my body has betrayed me. ||”|
It may be that the three-headed dragon is a part of the prince that was promised prophecy, and there are two other people whom the prince will need to have by his side, to show him the way.
Signs of the coming of the prince that was promised
- The birth of a male child - a prince. (erroneous according to Maester Aemon) 
- The prince is of the blood of the dragon. 
- Born amidst smoke.  
- Born amidst salt.  
- A bleeding star in the skies.  (also mentioned is being born beneath a bleeding star )
- The return of dragons? (when he was a boy Aegon V recalled that King Aerys read about the return of dragons in a prophecy.) 
- The dark eye falls upon the prince?
The prince that was promised theories
Main article: the prince that was promised/Theories
A Clash of Kings
Daenerys Targaryen's elder brother Prince Rhaegar appears in one of her visions in the House of the Undying in Qarth. She sees him talking to his wife Elia discussing what he shall name his son (Aegon) and his destiny. He states,
|“||"He is the prince that was promised, and his is the song of ice and fire.” ||”|
He looks up when he says those words and his eyes meet Dany’s, though whether he is speaking to her or the woman in the bed she cannot say.
Later, when down at the port of Qarth with Ser Jorah Mormont she discusses the vision with him. She mentions her brother said that the babe was the prince that was promised. Jorah observes that if he was this prince that was promised, the promise was broken along with his skull when the Lannisters dashed his head against a wall. Dany seems to accept this notion and goes on to ask what is the song of ice and fire but Jorah has never heard it. 
A Storm of Swords
On Dragonstone Melisandre tells Stannis Baratheon that he is "he who must stand against the Other". She tells him that he is the one whose coming was prophesied 5,000 years ago, the red comet was his herald and that he is the prince that was promised and that if he fails the world fails with him. 
|“||It is the war for the dawn you speak of, my lady. But where is the prince that was promised?||”|
Melisandre tells him that he is Stannis Baratheon, Azor Ahai come again, and that in him the prophecies are fulfilled.  Of note is that Melisandre does not reply that Stannis is the prince that was promised, she answers he is Azor Ahai.
A Feast for Crows
In Braavos, after Samwell Tarly tells Maester Aemon of the rumors about Daenerys Targaryen and her dragons, Aemon becomes convinced that Daenerys is the prophesied leader.  Maester Aemon states to Sam,
|“||Daenerys is the one, born amidst salt and smoke. The dragons prove it.||”|
A Dance with Dragons
In Meereen Ser Barristan Selmy talks to Dany about her mother and father. He mentions that her grandsire commanded that they be wed after a woods witch had foretold that the prince who was promised would be born of their line.  Dany is astonished by the fact that her grandsire listened to a woods witch and asks Ser Barristan about her, when Barristan mentions Summerhall she sighs and tells him to leave. Dany never asks him about the prince who was promised or makes mention of her vision in the House of the Undying to Ser Barristan.
|“||No one ever looked for a girl ... It was a prince that was promised, not a princess.||”|
|“||"She talks of prophecies...a hero reborn in the sea, living dragons hatched from dead stone...she speaks of signs and swears they point to me. I never asked for this , no more than I asked to be king. Yet dare I disregard her?" ||”|
|“||“Maester Aemon believed that Daenerys Targaryen was the fulfillment of a prophecy …..her, not Stannis, nor Prince Rhaegar, nor the princeling whose head was dashed against the wall. ||”|
|“||“Born amidst salt and smoke, beneath a bleeding star. I know the prophecy.” [he spits a gob of red phlegm onto the floor] “Not that I would trust it.” ||”|
References and Notes
- ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 A Feast for Crows, Chapter 35, Samwell.
- ↑ 2.0 2.1 2.2 A Storm of Swords, Chapter 54, Davos, p 711.
- ↑ 3.0 3.1 3.2 A Clash of Kings, Chapter 48, Daenerys.
- ↑ A Dance with Dragons, Chapter 40, Tyrion, page 534.
- ↑ 5.0 5.1 5.2 5.3 5.4 A Feast for Crows, Chapter 45, Samwell.
- ↑ The Mystery Knight,Warriors 1, ISBN 978-0-7653-6026-7, page 282 of 251-394.
- ↑ A Clash of Kings, Chapter 63, Daenerys.
- ↑ A Storm of Swords, Chapter 78, Samwell.
- ↑ A Dance with Dragons, Chapter 23, Daenerys.
- ↑ A Storm of Swords, Chapter 54, Davos, p 601.