A child born with a veil over her face is born with the amniotic sac unbroken during birth with the head still covered in the membrane or "veil." It is more common with natural births. It very rarely happens in the hospital because the water is often broken artificially.
A veil is also called a caul. Both are folk terms describing the amniotic sack or amnion when it covers the infant's head or face. A somewhat unusual occurrence with very rare health consequences, a child's birth with a veil (or caul) has been a traditional source of much folklore and superstition.
The veil was referenced in the poem "Infant Sorrow," by the poet William Blake. In England, the Pitt Rivers Museum, which specializes in English folklore, has several artifacts associated with a cultural obsession with veiled birth. One, a glass rolling pin dating to 1855, is said to have once contained a child's caul, then considered a sailor's charm. In Charles Dickens' classic "David Copperfield," published in monthly installments from 1849 to 50, the protagonist's caul is auctioned off as a talisman to prevent drowning.
Children born with this veil have traditionally been considered blessed, exceptional or gifted. The association of the caul with protection from drowning or safety at sea is especially prevalent.