Scurvy is a disease that happens from a lack of Vitamin C. In the game, when your crew mates haven't eaten any fruit for a while they have the possibility to get scurvy. When playing with the option "A plague that killed many innocents. (Plague)" your crewmen will be more susceptible to Scurvy. Scurvy is noticeable as the inflicted crew member will quite rapidly lose health. If enough health is lost your character will die like any other damage taken.
Scurvy can be cured by eating fruit like citrus.