The Bowman's membrane (Bowman's layer, anterior limiting lamina, anterior elastic lamina) is a smooth, acellular, nonregenerating layer, located between the superficial epithelium and the stroma in the cornea of the eye.
Source : Wikipedia
It was discovered in the mid 1800s, and is made of collagen fibres - apparently randomly orientated. It's normally 8-12 μm thick, but tends to thin with age.
Its function is unknown, but it's suggested that it may have some kind of protective function for the cornea.