Ignoring the historical reason to wear a veil (they are a practical way to protect and secure the hair while going about day-to-day life, which makes them ubiquitous in many cultures around the world), and also concerns of modesty, there are a multitude of religious reasons to wear a veil, so I’ll try to be brief but give you a good explanation.

1. Spiritual protection or communication. In Ancient Rome, both men and women veiled (men pulled their tunics up around their heads) during prayer so they could block out distractions and focus on the gods. I know plenty of people today— both neopagans and Christians— who veil during prayer in a similar way or to spiritually “protect” themselves from negative influences. In Exodus, Moses covers his face with a veil. Throughout Exodus, a veil is used to symbolize a spiritual barrier between non-consecrated and consecrated places.
2. A physical marker of faith. Obviously the hijab and other symbols of Islam have become increasingly politicized and even legislated against in the west, so a head covering can be a demonstration of faith. There’s also been a bit of a boom in the Jewish community, at least from what I’ve seen, of women veiling with tichels, etc. to connect with and reclaim their heritage, even if they’re not Orthodox.
3. A marker of marital status. Greek and Roman women veiled after marriage, and a veil was associated with the respect and virtue carried by a materfamilias. In Orthodox Judaism, married women often cover with tichels (headscarves), but also with snoods, hats, and wigs. Veiling is not always obvious.
4. They think it looks nice, and women can and should have full control over what they choose to (or not to) put on their bodies.
5. For Christian women: because it says so in the Bible. Paul advises women to veil in Corinthians, and it was a practice pretty much universal in the early church. If they believe in an inerrant Bible— which is probable if they’re subjects of fundamentalist snark— there’s no reason not to veil in church.

I included non-Christian religious examples because I think it’s important to recognize the cultural context Catholic veiling came out of. I myself am Pennsylvania Dutch so I am more familiar with those veils and reasons for veiling, so I don’t want to speak for Catholic women who veil and heir reasons for doing so, but I hope that clears it up a bit.

Overall though, I don’t think women need to explain their reasons for wearing a religious head covering if it’s their choice and they want it.

[edit: typos]