For me it has two main purposes:
One is to sort of 'get myself in the mood' for prayer, a bit like we (by which I mean people from many different faith traditions) often ring a bell at the beginning and end of meditation. It signifies a sacred space and time, and I remind myself of that with my body. I often remove my shoes too, for the same reason (and because I hate shoes and am much more comfortable without
).
Secondly it's a sort of 'do not disturb' sign to others. Because I work in the church I often get people who think that when they see me kneeling with my eyes closed is a perfect time to ask about the dress code for first communion or to pass a message on to someone else. The veil helps filter a few of these out, although I still get some.
Additionally, although this is by no means the primary motivation, it does give me a bit of a sense of solidarity with the centuries of women in the Church before me. Plus, if i wear a mantilla then it cuts out a bit of my peripheral vision so I concentrate better!