Despite the fact that its inclusion of spaceships and different types of people from different planets makes Star Wars sci-fi, I think of it more as fantasy. The Force is akin to magic, the lightsaber duels are akin to sword fights, and what's the difference between aliens and fantastical creatures anyway? Oh, yes, and there's even the awakening of a character from sleep like death.
Not Prince Philip waking Sleeping Beauty, no, in Star Wars it is the princess who does the waking.
Han Solo isn't quite in an enchanted sleep and he isn't under a curse, but the chief villain has put him into a sleep from which he cannot wake on his own. Darth Vader has allowed Boba Fett to deliver Han Solo to Jabba the Hutt; he is consequently well-guarded in his deep sleep. So he might as well be in an enchanted sleep.
Enter Leia in a carefully-organized plan of rescue. Her role: to wake Han. Not to get him out--just to wake him. That is enough. True, it is the pressing of buttons on the panel that ends the hibernation, not her kiss, but that's a mere technicality. The image of her waking him remains. The princess waking her love from his death sleep.
Other than the simple image, there are a couple of other things to note about this waking. It proves that just because one character, at some point, needs the other one to wake him/her, that does not mean that he/she is weak. Do you know what I mean? Sometimes princess stories get hate because people say they portray women as needing to be saved by men. Maybe that's true--but that isn't the only way to interpret these stories. Especially Sleeping Beauty. That's a movie about two people who meet and fall in love and then encounter some dangers, after which the prince happens to be the one who is awake and therefore able to help the princess. It's like that with Star Wars: no one would call Han Solo a weak character (in that sense of the word--he is sometimes weak, towards the beginning, with his self-centeredness and his love of money), yet at this point in the story he needs saving from Leia.
The second thing is the reversal of roles and the fact that it is not isolated to this one scene. In contrast to the idea of princesses who need saving from men, Leia often helps Han, as he often helps her. When they first meet, for instance, she is the one who takes the gun and opens up a way for them to get into the garbage disposal area to escape from the detention section. Leia is never one to be passive; after all, she is one of the leading figures of the rebellion and no passive person would even be part of the rebellion, much less help lead it.
So we return to the image: the man who has been put under a deep sleep from which only his love, the princess, can wake him.