A tall lord with copper skin and silver-gold hair stood beneath the banner of a fiery stallion, a burning city behind him.

This appears to be a vision of what might have been had Rhaego survived to be the Stallion Who Mounts the World. As stated by Melisandre and Thoros, prophetic visions can show what may be rather than what will be, although this is not invariably the case (Jojen claims his green dreams always come true).

Rubies flew like drops of blood from the chest of a dying prince, and he sank to his knees in the water and with his last breath murmured a woman's name.

This is a depiction of a past event, Rhaegar's death at the ruby ford of the Trident at the hands of Robert Baratheon. The only thing of real importance is the fact that he utters a woman's name. Many believe this name to be Lyanna, signifying that Rhaegar's relationship to Lyanna Stark was much more complex and heartfelt than previous indications in the books might show.

Glowing like sunset, a red sword was raised in the hand of a blue-eyed king who cast no shadow.

This appears to be a present event. The red sword would seem to be Lightbringer, the Red Sword of Heroes, and the blue-eyed king without a shadow would then be Stannis Baratheon whose shadow has been so recently harnessed by Melisandre's sorcery to murder Renly Baratheon and Ser Cortnay Penrose. It is likely that Stannis's claim to being Azor Ahai reborn, and his role in the war against the Others, will have a serious impact on Dany's future.

A cloth dragon swayed on poles amidst a cheering crowd.

As Dany later states, this is a mummer's dragon. What this signifies is unclear. It may be that in time a mummer's dragon will be a sort of standard for Dany and her army. It is useful to note that Martin has indicated that a character known as the King of the Mummers will appear in the series in the future.

From a smoking tower, a great stone beast took wing, breathing shadow fire.

Clearly tying in both to Shireen's dreams of the stone dragons of Dragonstone eating her, and Melisandre's plan to use king's blood to bring a stone dragon to life, the fact that Dragonstone lies nearly abandoned by Stannis makes it much more difficult to understand. Could this be an image of something that may have been, but due to Davos's sudden intervention was averted? Another and completely unrelated possibility -- albeit it not a likely one -- is that the vision may represent a dragon that was awakened at the razing of Winterfell. While an interesting theory, the "shadow fire" does not seem to fit.

Her silver was trotting through the grass, to a darkling stream beneath a sea of stars.

This is almost certainly depicting Daenerys's wedding night under the stars with Drogo. Many major developments in her life followed from this time.

A corpse stood at the prow of a ship, eyes bright in his dead face, grey lips smiling sadly.

A true mystery, the figure is thought to perhaps represent Theon Greyjoy after escaping his fate at the hands of the Boltons, Gerion Lannister, and even Davos Seaworth. In the case of the Gerion, the bright eyes in a dead face may represent the fact that he is alive despite the common belief that he was lost at sea. Another fringe possibility is that the figure is someone like Coldhands, a sentient and autonomous wight, but this does not answer who it might be or why they would be aboard a ship.

A blue flower grew from a chink in a wall of ice, and filled the air with sweetness.

An image of major importance to many readers, it is commonly believed that this vision draws a direct connection between Lyanna Stark (who loved blue roses), the song of Bael the Bard (who eloped with Lord Stark's daughter, leaving a blue rose in her place, and had a child by her), and Jon Snow (who is on the Wall). If the reading is correct, it is one of the strongest pieces of evidence in support of Jon being the son of Rhaegar Targaryen and Lyanna Stark. An alternate but less popular explanation is that the blue flower merely represents a Stark on the Wall.

In either case, the air being filled with sweetness suggests that Jon Snow is of great importance to Daenerys, and it may tie into the possibility that they will fall in love later in the series.

Shadows whirled and danced inside a tent, boneless and terrible.

This is probably Mirri Maz Duur's ceremony which apparently destroyed the unborn Rhaego and left Drogo without a mind, an event which directly led to the birth of Dany's three dragons. A more remote possibility is that it represents Melisandre's conjuring Stannis's shadow to slay Renly.

A little girl ran barefoot toward a big house with a red door.

This certainly seems to represent Daenerys as a little girl, going to the house in Braavos where she had felt safest and most protected in her life. Given events in A Storm of Swords, however, this may well represent Arya Stark running towards such a door in Braavos for some unknown reason. Certainly, there is no suggestion of Daenerys recognizing the girl.

Behind a silver horse the blood corpse of a naked man bounced and dragged.

This almost certainly is a vision of the past, when Daenerys dragged her would-be assassin behind her.

A white lion ran through grass taller than a man.

This could represent the hrakkar which Drogo hunted just as an attempt was made on Dany's life, but this seems very mundane. A more popular suggestion is that this may represent Jaime Lannister, a White Sword and a lion of Casterly Rock. Another is that it might represent a Lannister, but Tyrion Lannister rather than Jaime. The white could then represent his very pale hair, and the tall grass may actually be quite mundane but for the dwarfish lion that has come forward.

Beneath the Mother of Mountains, a line of naked crones crept from a great lake and knelt shivering before her, their grey heads bowed.

This does not seem to have been fulfilled, and may in fact suggest that in the future Dany will win the loyalty of the dosh khaleen and the Dothraki. Or, like the vision of Rhaego, it may represent her status had Rhaego survived.

Ten thousand slaves lifted bloodstained hands as she raced by on her silver, riding like the wind. "Mother!" they cried. "Mother, mother!" They were reaching for her, touching her, tugging at her cloak, the hem of her skirt, her food, her leg, her breast. They wanted her, needed her, the fire, the life, and Dany gasped and opened her arms to give herself to them.

This has been fulfilled with Dany's liberation of the slaves of Yunkai in A Storm of Swords.