Ringworm is a skin condition that's not uncommon in horses. It causes circular patches of hair to fall out. The infection then spreads outwards and the hair grows back in the center, hence the name.
Ringworm is caused by one of a number of species of fungus. It is highly contagious - it's not unknown for the entire barn to get it, sometimes before handlers realize a single horse is infected.
Left untreated, ringworm generally goes away in a few weeks, but horses can be re-infected and continue to infect each other. In modern times, it's generally treated with an anti-fungal wash (it's not uncommon to have to try two or more) which is applied after thorough cleaning. Severe cases may receive oral medication.
Ringworm can be transmitted to other animals, including humans, so handlers wear disposable gloves when treating it. (The treatment for humans is the same as for horses).
In lower tech levels, ringworm (see the name) is probably mistaken for some kind of parasite and its contagious nature may or may not be known. It's highly annoying but seldom serious.