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 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. 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 until the end of 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 21, his countdown truly began as the rose slowly but surely began to wilt. However, he managed to bring to his castle a beautiful village girl named Belle. Over time, they grew close until at last, through various events, Belle admitted she loved him just before 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.