The Enchanted Rose is a mystic flower from the 1991 Disney animated film, Beauty and the Beast. The Enchanted Rose has since become the trademark symbol for Beauty and the Beast.
When the Beast was a human prince, an old beggar woman came to his castle requesting shelter from the bitter cold and offered to him this very rose. The prince sneered at the gift and turned the old woman away because of her haggard appearance. She warned him not to judge her based on appearance for true beauty was found within. When he did not heed her warning, she shed her false form, revealing herself to be an astonishingly beautiful enchantress.
She saw that there was no love in the prince's heart, and thus punished him by turning him into a Beast, and all who dwelt within the castle into living objects, as well as cursing the castle itself and possibly the surrounding forest. She left him the rose, promising him that it would bloom until his 21st year: If he could learn to love and earn in love in return before the last petal fell, the spell would be broken. If he failed, he would be doomed to remain a beast for all time.
Ever since, the Beast kept the rose safe in his chambers, the rose serving as his countdown and a reminder of his selfishness and cruelty.
When the Beast finally turned 20, his countdown truly began as the rose slowly but surely began to wilt. At the end of the film, the Beast appears to reach the deadline of his 21st birthday because the rose completely finishes wilting.
Aside from the prologue, the enchanted rose made its first appearance after Beast's failed attempt at convincing Belle to come have dinner with him. After Beast overheard Belle's comment about not wanting to have anything to do with him and being hurt by the remark, a petal fell down. During this scene, it was revealed that at least four petals fell before that one, and Lumière beforehand mentioned that the rose had started wilting months prior.
The rose was later seen again when Belle entered the West Wing without the Beast's permission, where she briefly saw it and then proceeded to remove its glass covering before attempting to touch its petals. However, the Beast caught her and snapped at her due to her actions nearly destroying the rose by accident, yelling at her to get out of the West Wing (although she ended up leaving the Castle as well, necessitating Beast to save her).
The rose appears in the background for the remainder of the film, and is seen one last time as Beast dies and Belle professes her love for him just as the last petal fell. The Beast had succeeded; the spell was broken, restoring him and his servants to their human forms, and the bleak fortress into a shining castle. The Beast-turned-Prince married Belle and they lived happily ever after.
In the Special Edition, the rose was also carried by the podium (which is revealed to also be possibly sentient, though whether it was originally human or just an object given life is never revealed) to the main foyer during Cogsworth's briefing, just before the song "Human Again". It is also in this scene that Cogsworth states the amount of time it will take by then before the final petal falls, of which the rose is already down to its last petal.