Way back in the "olden days," brides would wear veils to ward off evil spirits.
Later, it was to symbolize the bride's purity and modesty (aka virginity).
Now, it's more for the dramatic style it gives a bride, and as a nod to the past traditions.
The father of the bride is usually the one to lift the veil off the face of the bride - which is a sweet moment and great photo op! Or, the veil can be left covering the face, and it isn't until the groom goes in for the KISS that is gets lifted.
But, the bottom line is: You don't have to cover your face with a veil if you don't want to.
Single-layer veils can be worn just down the back of the hair. After all, the side and back are the most visible areas on the big day!