The stole is a scarf that was used as a symbol of authority for Roman officials. It would be something like the badge that a police or fire official wears today. The Catholic Church, when part of the Roman Empire, adopted the stole to indicate when a priest is engaged in his role as presider during the celebration of a Sacrament.
The colors for the vestments used in the celebration of sacraments and other liturgical events were selected by Pope Innocent III, a 12th century bishop of Rome, for their symbolism (white for Christmas and Easter, red for the feasts of martyrs and the Holy Spirit, green for ordinary time, and purple for Advent and Lent). They also evoke a particular mood. The color purple has a cool, calming effect which lends itself to the quiet, reflective moods of Advent and Lent. Purple is associated with penance and with healing.
Exorcisms, as popularized in many Hollywood movies, are actually extremely rare in the Catholic Church, while the sacrament of Reconciliation (confession) is a regular part of the Church’s life. Both exorcism and confession involve a ritual praying for the healing of a person from the power of evil and a reunion with the Christian community. In that sense the healing color purple is appropriate as a sign of God’s healing power at work through the ministry of the priest and the prayers of the community.
I hope you’ll have a chance to discover the Sacrament of Reconciliation in its present form. It’s intended to be a concrete experience of God’s healing and forgiveness. Catholics who go to confession today tend to leave feeling glad that they decided to do so. And many go during Advent time as Catholics are required to go a least once a year to confession.