Head covering for women in church rests on 1 Corinthians 11, which is one of the more disputed passages in the Pauline letters, and was for centuries simply what Catholic women did. The 1917 Code of Canon Law made it a requirement in law.
The 1983 Code did not repeat it. In the intervening decades the practice had largely disappeared from ordinary parish life across Europe and the Americas, quickly and without much argument at the time, alongside a great deal of other change following the Second Vatican Council. By the 1980s a woman veiling at an ordinary parish Mass was unusual.
It has returned, and the return is deliberate. It is concentrated among younger women attached to the traditional Latin Mass, and it is visible enough to have become a marker. Those who wear it describe it variously: as a personal devotion, as a response to the presence of the Eucharist rather than to anyone in the congregation, as a reclaiming of something they judge to have been discarded carelessly rather than decided against. Others in the same church read the revival as inseparable from a wider set of positions about women's roles and about the liturgical reforms generally, and say so.
The disagreement is entirely internal to Catholicism, both sides are Catholics in good standing, and no rule currently compels or forbids either practice. It is worth setting down accurately because it is frequently reported from outside as either a quaint survival or a symptom, and it is neither.