How are cells of the cornea transparent?
Most cells are transparent, which is why we can see cells using bright-field microscopy, where the light travels through the cells before you see it. That's how we can see inside onion cells and see structures like onion cell nucleii, moss cells, human epithelial cells and animal mast cells.

The human cornea is made up of five layers, each of which have different structures allowing them to be transparent: the outer and inner epithelial layers are very thin and naturally pretty transparent, and the middle layers have collagen fibres; based on that Wikipedia article, it sounds like there are several hypotheses for why these layers are transparent, but it doesn't look like there's a definitive answer yet.