These other questions may be interesting:
I want to add to the answers provided by /u/mimicofmodes and /u/cecikierk provided in the linked answers /u/sjoerder references.
/u/cecikierk gives the "legal" answer regarding the Canons (law) of the Catholic Church that essentially regulate behavior and provide a framework from within the Catholic Church operates. To give context as to why the Catholic Church felt it could "change" the "practice found in Scripture" requires a deeper understanding of what Scripture is and how it is viewed, what the Church is, and what the tradition of head-coverings represent.
Not everything in Scripture carries the force of moral (e.g. universally binding) law. The Scriptures were written at a particular time and place for a particular people by a particular people - Scripture contains not only moral laws (e.g. the Ten Commandments), but the history of the people of Israel - the path divine revelation took and the ceremonial and judicial law that governed their everyday lives. This is part of the reason modern Christians no longer observe the ceremonial or judicial laws of the Old Testament (i.e. parts of Leviticus, often wrongly cited on internet forums to point out the "hypocrisy" of Christians in not obeying every facet of first century Jewish law), and key in understanding the passage in Corinthians. Paul was writing to the Church at Corinth, a commercial city on the Aegean sea. Over time, the Corinthians (likely due to the pressures of being a cosmopolitan city, the overwhelming presence of Paganism, and the arrival of new Jewish converts from elsewhere) had adopted a number of problematic positions requiring both doctrinal and disciplinary correction by Paul - among them, visits to pagan ceremonies, the nature of the Eucharistic celebration, and liturgical abuse. To this latter point, the Corinthians had apparently began violating gender norms by mixing the sexes in ways that gave scandal, e.g. gender-appropriate dress code. Commentary from the Ignatius Study Bible does a really nice job of summing up the issues:
11:3-16 ...It seems that the Corinthians have challenged the distinction between the sexes by violating gender-appropriate dress codes in the liturgy. Paul's guidelines imply that the order of redemption, where men and women are equal recipients of grace (Gal 3:28), does not obliterate the order of creation, where gender differences are written into nature (Gen 1:27).
11:6 veil herself: Many believe the veil symbolizes the subordinate status of women that should be reflected in a liturgical setting (14:34). The Catholic Church teaches that Paul's counsel on the veiling of women was inspired by the customs of the day. Because this was a matter of discipline, not doctrine, the Pauline directives on covering and uncovering the head are subject to change. They are no longer binding on men and women today (Sacred Congregation for the Doctrine of the Faith: Inter insigniores [1976], 4).
Two things here - first, the citation references a difference in understanding between "discipline" and "doctrine" within Scripture. These words reflect the understanding (already discussed) that Scripture not only contains judicial law (e.g. discipline) but moral law (e.g. doctrine); the former is not universally binding (customs may change), whereas the latter is (morality does not change). The next logical question is "well, who gets to determine what is discipline and what is doctrine?"
The Catechism of the Catholic Church answers this question, and which I reference in this reply to a subscriber who is in error concerning their understanding of the word "tradition" as applied to customs and those things which have the force of moral law (what Catholics often refer to as "'little t' traditions and 'big T' Sacred Tradition"). The short of it is that the Magisterium (i.e. teaching authority) of the Church, by virtue of its divine origin (e.g. an apostolic ministry [remember, Paul was an apostle] founded by Christ and handed on to the present day [e.g. pope Francis is one of a long line of popes, tracing their lineage to Paul's contemporary, Peter]), is entrusted with authentic interpretation of both Sacred Scripture and Sacred Tradition.
All that said, this builds to the citation from the commentary - that of a document authored by the Congregation for the Doctrine of the Faith, the ecclesial office responsible for correcting errors in the understanding of discipline and doctrine - in issuing this document, this office is exercising a type of Magisterial authority. The document itself, Inter insigniores, is available online, and has the subtitle "On the question of admission of women to the ministerial priesthood" - it is essentially a response to individuals who had begun to teach that the prohibition on women's ordination was merely disciplinary in nature (e.g. a result of social conditions in the first century), and had no doctrinal force. This is another discussion, but the pertinent part of this document to further answer your question can be found within it:
Another objection is based upon the transitory character that one claims to see today in some of the prescriptions of Saint Paul concerning women, and upon the difficulties that some aspects of his teaching raise in this regard. But it must be noted that these ordinances, probably inspired by the customs of the period, concern scarcely more than disciplinary practices of minor importance, such as the obligation imposed upon women to wear a veil on their head (1 Cor 11:2-16); such requirements no longer have a normative value.
The declaration goes on to address a number of other issues, but the tl;dr of the whole thing is that the admonition of the Corinthians by Paul for women to wear head coverings is not a doctrinal issue, but one of discipline, and that in failing to abide by these ('little t') liturgical and cultural traditions the Corinthians were unnecessarily splitting their congregation and causing scandal among the faithful of the day. In the modern era (as /u/mimicofmodes's answer really starts to lay out), these cultural and liturgical concerns are less pressing, and thus the new Canons (i.e. the Law of 1983, as /u/cecikierk cited) abrogating the old requirement (from the Law of 1917).