To start off I just had a really funny thought! What if all the evil in Jaime Lannister's body was contained in his sword hand!
So when they cut it off, he turned good lol. In all seriousness though, it seems at least symbolic of that. His sword hand, with which he has perpetrated so much evil, has been taken from him and he's forced to re-evaluate himself as a man.
I also found this nifty someone had made of all Dany's visions in the house of the undying.
"1) a scene where four men with rat faces are raping a beautiful woman;
2) a feast of corpses, where many of the bodies were savagely slaughtered, and many of the corpses have cups or spoons in their hands; above them sits a dead man on a throne with the head of a wolf, wearing an iron crown and holding a leg of lamb like a king would hold a scepter;
3) old, dead, loyal Ser Willem Darry at the house with the red door from when Daenerys lived in Braavos;
4) a scene where an old man with long silver hair sits on a barbed throne in a great hall with dragon skulls, and says "Let him be the king of ashes";
5) a man who looked like Viserys, but taller and with darker eyes, who says to a woman nursing a baby, "Aegon…What better name for a king…He is the prince that was promised, and his is the song of ice and fire"; and when the man’s eyes meet Dany’s, he says either to her or the woman with the baby, "There must be one more…The dragon has three heads", and he picks up a silver harp and begins to play;
6) a vision of Pyat Pree telling her the visit was over, and to follow him into a garden;
7) a great hall with several robed people claiming to be the Undying of Qarth, who tell her, "We sent the comet to show you the way (to Qarth)…shall we teach you the secret speech of dragonkind?", but it turns out to be sorcery.
8) Viserys dying;
9) a tall lord with copper skin and silver hair bearing the banner of a fiery stallion (probably Rhaego, her unborn son); 10) a dying prince with rubies flying from his armor whispering the name of a woman with his last breath;
11) a blue-eyed king with a red sword in his hand who cast no shadow;
12) a cloth dragon amidst a cheering crowd;
13) a great stone beast flying from a smoking tower, breathing shadow fire;
14) her Silver horse given to her by Drogo at her wedding;
15) a corpse at the prow of a ship, eyes bright in his dead face, smiling sadly;
16) a blue flower growing from a chink in a wall of ice;
17) shadows dancing in a tent;[1]
18) a little girl running toward a house with a red door;[2]
19) Mirri Maz Duur shrieking in the flames as a dragon bursts from her;
20) a corpse being dragged behind a silver horse;
21) a white lion running through grass taller than a man;
22) a line of naked crones emerging from a lake, kneeling before Daenerys beneath the Mother of Mountains;
23) ten thousand slaves crying "Mother" as Daenerys rode by on her silver.[3]
Some are fairly obvious but others are still kind of vague and unclear as of this point in the series. I'm interested in #16 the blue rose in the ice wall, as it points to Jon being Lyanna's son and possibly the third head of the dragon. A lot of people on some other forums seem to think Aegon is a fake? I don't see that though, he wouldn't have a knight of Westroros with him if he was a fake and he has the signature blonde hair and purple eyes.