Three of them, specifically.
The Veil of Maya in Hinduism is the symbol of illusion, dreaming, and duality. It cloacks true reality from us, replacing it with illusions, distracting colors and shapes. The goddess Maya is also the protector of the universe who possesses a part of every other god's and goddess' power. I don't know about you, I like illusions.
The féth fíada is the magic mist or veil that cloaks the fae world and its inhabitants from mortal eyes. In one of my favorite Irish stories Eithne lost her veil as she was bathing in a stream, and after that she could never find her way home to her own world; it was invisible to her eyes, and she to theirs. She became a nun and took on Christianity before she died.
And then there is a third one, called The Wedding Veil of the Proud Princess, written by Lucy Maud Montgomery in her book The Story Girl, which is largely responsible for me becoming a professional storyteller (go figure). It is a tale about the princess who is too proud to marry any mortal man; she waits for a knight that defeats everyone. Well, she ends up marrying a mysterious victor in black armor... read the rest for yourselves!
This story always reminds me of this song which is based on a similar tale:
Der Letzte Tanz (Schandmaul)
One of my favorite songs. That's all!