Catherine was a noble maiden of Alexandria, who from her earliest years joined the study of the liberal arts with fervent faith, and in a short while came to such an height of holiness and learning, that when she was eighteen years of age she prevailed over the chiefest wits. When she saw many diversely tormented and haled to death by command of Maximinus, because they professed the Christian religion, she went boldly unto him and rebuked him for his savage cruelty, bringing forward likewise most sage reasons why the faith of Christ should be needful for salvation.
Here is a legend of it. Picture to yourself a lovely, fiery young woman, unmarried not even twenty-five, devout and intelligent, of a noble family of Alexandria. From her earliest years she had studied all she could learn with great precociousness. Such a woman was Catharine.
During a great persecution of Christians, Catharine went to the king to upbraid him for his injustice, and lectured him with a long philosophical discourse on the iniquity of idolatry and the rationality of the worship of the one true God. The despot, astounded by her audacious behavior, but intrigued by her skill, summoned a group of orators to compete with her. And so they tried; but their worldly rhetoric could not compare with the eloquence of Catharine, simple, saintly, and wise. Several became Christian. They were slain.
Frustrated, the tyrant summoned a group of philosophers to persuade her of her folly. And so they tried; but their pagan reasoning, contaminated with superstition, could not compare with the reasoning of Catharine, simple, saintly, and wise. Several became Christian. They were slain.
It was unacceptable; the king ordered her put to death for sympathizing with his enemies. She was meanwhile thrown into prison, and there she was visited by one of the emperor's favored women, along with the head of the emperor's guard. She spoke to them of the needfulness of Christ, of the coherence of all the universe in Him, of the Word who was with God and who was God. They were converted and baptized in secret; but the emperor found out, and in a rage had them both killed. The despot knew he could not afford to delay. He ordered that she be immediately broken on the wheel, a terrible death of intense suffering. She was placed upon it and the wheel began to turn. Slowly, ever so slowly, with great force it began to pull her apart; but hardly had it started when it broke. Ever since the Broken Wheel has been the chief symbol of Saint Catharine. She was thrown into the fire; the fire would not burn around her. So a sword was brought, and some say it was thrust into her side, while others say she was beheaded with it. But the sword slew her, and thereby she gained the martyr's palm and crown.
You can read more about her legend at the Catholic Encyclopedia and also here.