Why do some women wear a veil when in a Catholic church?

Since the early days of Christianity, wearing chapel veils has been a common practice among faithful women. Chapel veils, also commonly called mantillas, which comes from the word manta, meaning cape, are typically circular or triangular shaped pieces of black or white lace that are draped over a woman’s head when attending Mass, or in the presence of the Blessed Sacrament. Traditionally, the black veils were worn by married or widowed women, while the white veils were worn by young girls, or unmarried women. 
 
Throughout the centuries, the use of the mantilla by women has had many purposes. The wearing of the mantilla is an act of veiling a woman's physical beauty (as a woman’s hair is traditionally considered her crowning beauty), so that the beauty of God may be glorified instead. It is also a way of emulating Mary, our mother, who is the archetype of purity and humility. Moreover, the mantilla, or chapel veil, signifies the role of women as a life-bearing vessel. Oftentimes, the chalice holding the blood of Christ is veiled until the Preparation of the Gifts, and the tabernacle is veiled between Masses. Both of these vessels hold the Eucharist – the very life of Christ. In a similar fashion, the woman was endowed by God with the special gift of bearing new human life. Because of this, women, as all things holy and sacred, are veiled. 
 
Before the Second Vatican Council, the wearing of chapel veils was required for a woman when attending Mass, as a symbol of her modesty and humility before God. Although this practice is no longer required, it is still very much supported and encouraged by the Church as a sign of reverence and piety while in the presence of God. 
 
In addition to being a long-standing and beautiful piece of our Catholic tradition, there are three great reasons to wear a mantilla: (1) veiling is a physical reminder that you are entering a Sacred space, (2) veiling is a sign of feminine dignity, and (3) veiling is half of a dual-tradition whereby a woman covers her head (by covering her hair with a veil), and a man uncovers his head (by removing his hat) when entering a church as a sign of humility and devotion.