Along with St. Patrick, St. Brigid of Kildare is known as a co-patron of Ireland, having been a close collaborator of the missionary bishop. She was highly influential in the early years of Christianity on the Emerald Isle and established many monasteries of religious women.
What's interesting is that often in art she is depicted with a crosier, also known as the bishop's staff.
Why is that?
The shepherd's staff
First of all, the crosier used by a bishop is meant to symbolize his pastoral leadership of a local area. He is the spiritual shepherd of a particular region, and the staff is meant to recall Jesus, the Good Shepherd, who guides his flock.
The crosier is an ancient custom, dating back centuries in the Church, and continues to be used by bishops around the world.
Female shepherds
In a similar way, many nuns who held positions of leadership in their religious orders would be given a staff, representing their pastoral leadership of a group of women. A woman who supervised an abbey of women was known as an abbess, and had much of the same religious symbolism as her counterpart, an abbot, in a men's religious order.
The Catholic Encyclopedia explains this symbolism.
St. Brigid, Shepherdess of Ireland
St. Brigid held a prominent role in the formation of Christianity in Ireland, and not only directed her religious nuns, but also helped guide local dioceses.
The Catholic Encyclopedia also clarifies her role in Ireland.
St. Brigid was instrumental in the establishment of Christianity in Ireland, and her depiction with a crosier highlights this reality.