"Traditionally the ‘veil’ or ‘mantilla’ represented purity and modesty in many religions and cultures. A veil, or head covering, is a symbol that can enable the woman wearing it to ascend the ladder of sanctity. When a woman covers her head in the Catholic Church it symbolizes her dignity and humility before God, not men.
The woman who covers her head in the presence of the Lord Jesus in the Blessed Sacrament is reminding herself that she must be humble before God. As with all outward gestures, if it is practiced enough it filters down into the heart and is translated into actions that speak volumes. The “veil” covers what the Lord calls, in Holy Scripture, “the glory of the woman”, her hair. Covering her hair is a gesture the woman makes spiritually to “show” God she recognizes her beauty is less than His and His Glory is far above hers. In doing this she is reminded that virtues cannot grow in the soul without a great measure of humility. So she wears the veil to please God and remind herself to practice virtue more ardently."