Cotto means 'cooked, but if you see it by itself on a menu, it means prosciutto cotto (cooked rather than cured ham).
When ordering meat in a restaurant you may be asked for la cottura:
al sangue (or poco cotto): rare
a media cottura: medium rare
rosata: medium ('pink')
cotto a puntino: cooked to perfection (according to the chef)
ben cotto: well-done. Never for a bistecca alla fiorentina!
Other terms:
cotto a bassa temperatura: cooked at a low temperature (often sous-vide, or cucina sottovuoto)
cottura arrosta: roasting
cottura a fuoco lento: simmering
cottura in umido: stewing
For fish, use poco cotto, cottura media, or ben cotto.
Image by Birte, Public Domain