A caul is a thin, filmy membrane

Biological membrane

A biological membrane or biomembrane is an enclosing or separatingmembrane that acts as a selective barrier, within or around a cell. It consists of a lipid bilayer with embedded proteins that may constitute close to 50% of membrane content...

, the amnion

Amnion

The amnion is a membrane building the amniotic sac that surrounds and protects an embryo. It is developed in reptiles, birds, and mammals, which are hence called “Amniota”; but not in amphibians and fish , which are consequently termed “Anamniota”. The primary role of this is the protection of the...

, that can cover a newborn's head and face immediately after birth.
A child "born with the caul" has a portion of the amniotic sac

Amniotic sac

The amniotic sac is the sac in which the fetus develops in amniotes. It is a tough but thin transparent pair of membranes, which hold a developing embryo until shortly before birth. The inner membrane, the amnion, contains the amniotic fluid and the fetus. The outer membrane, the Chorion,...

 or membrane

Amnion

The amnion is a membrane building the amniotic sac that surrounds and protects an embryo. It is developed in reptiles, birds, and mammals, which are hence called “Amniota”; but not in amphibians and fish , which are consequently termed “Anamniota”. The primary role of this is the protection of the...

 remaining on the head. There are two types of cauls. The most common caul is adhered to the head and face, and looped around the ears of the infant. The rarer type drapes over the head and partly down the torso of the child.