Thrush is a common bacterial or fungal disease that generally affects the sole of a horse's foot. (It is a different pathogen from the one which normally causes thrush in humans).
Thrush is most commonly found in horses that are stalled for extended periods of time, especially in moist or humid conditions. The best prevention is to keep stalls clean and avoid using deep bedding unless the situation warrants it (and to turn out as much as possible).
It's treated with thorough cleaning - often involving a bath in Lysol dilution or mild dish washing detergent). A topical bactericide or fungicide might also be used. Thrush generally takes a couple of weeks to clear up.
Thrush is not directly contagious from animal to animal and, contrary to popular belief, is also not contagious from animal to human. (I'll talk about some conditions that you can catch from a horse in the future).