It dates back to the ancient where according to the wedding historian, Susan Waggoner, "who wrapped the brides from head to toe is to represent the delivery of a modest and untouched maiden". It is almost similar to the reason why brides choose the color white for their wedding gown, to which it represent the symbol of purification. Aside from it, others also believe that the veil also hid the bride away from the evil presence who might want to thwart her happiness.
This question also draws back to the history of the wedding of Queen Victoria and Prince Albert where she dress herself in white and a veil cascading down her back, which once again making her the first modern monarch to be married in a veil. and from that moment, the image of a bride was defined for centuries to come.
More on: https://www.brides.com/story/wedding-traditions-debunked-the-veil