According to the Wikipedia:
"It was long supposed that she was a noble lady of Rome who, with her husband Valerian, his brother Tiburtius, and a Roman soldier Maximus, suffered martyrdom, c. 230, under the Emperor Alexander Severus.
The research of [nineteenth century archeologist] Giovanni Battista de Rossi, however, appears to confirm the statement of Venantius Fortunatus, Bishop of Poitiers (d. 600), that she perished in Sicily under Emperor Marcus Aurelius between 176 and 180. A church in her honor exists in Rome from about the 5th century, was rebuilt with much splendor by Pope Paschal I around the year 820, and again by Cardinal Paolo Emilio Sfondrati in 1599. It is situated in Trastevere, near the Ripa Grande quay, where in earlier days the Ghetto was located, and is the titulus of a Cardinal Priest, currently Carlo Maria Martini.
The martyrdom of Cecilia is said to have followed that of her husband and his brother by the prefect Turcius Almachius. The officers of the prefect then sought to have Cecilia killed as well. She arranged to have her home preserved as a church before she was arrested. At that time, the officials attempted to kill her by smothering her by steam. However, the attempt failed, and she was to have her head chopped off. But they were unsuccessful three times, and she would not die until she received the sacrament of Holy Communion.
Cecilia survived another three days before succumbing. In the last three days of her life, she opened her eyes, gazed at her family and friends who crowded around her cell, closed them, and never opened them again. The people by her cell knew immediately that she was to become a saint in heaven. When her incorruptible body was found long after her death, it was found that on one hand she had three fingers outstretched and on the other hand just one finger, denoting her belief in the trinity. The skull of Saint Cecilia is kept as a relic in the cathedral of Torcello."
She is patroness of music because she sang as she lay dying. Here's a snippet from Purcell's tribute to the saint:
