A grass crack is a crack in a horse's hoof that starts at the bottom and works upward.
Grass cracks are seen more often on unshod horses, and may or may not make the horse actually lame. They are caused by excessive moisture and are basically harmless, but they can spread up towards the top of the hoof. Some horses are more prone to them than others - and often horses that are particularly prone to cracking have to be shod. Aggressive trimming can also help reduce cracking (and poor trimming can cause it).
Another way to treat chronic cracking is to add biotin and calcium to the horse's diet to support better keratin production. (You may see biotin supplements in the drug store advertised as helping your nails and hair, but it hasn't been proven that they work in humans, who are less likely to be deficient in biotin than horses).
(Note that the term quarter crack is sometimes used to refer to a grass crack that occurs close to the heel, but it is also sometimes used to refer to sand cracks, which I'll talk about tomorrow).