Illness
Illness, like other conditions in dreams, is generally a metaphor for a psychological state. If one dreams that someone is ill, it likely means that what the figure represents simply isn’t "well" (perhaps due to repression).
More specific illnesses in dreams, such as cancer, are often better understood metaphorically by analyzing what the illness does to the body and translating that into psychological terms. For instance, cancer might symbolize some autonomous, unconscious process that is uncontrollably taking over. One can approach the character of the condition as a personality with the traits of the illness to begin understanding what it reflects in the dream. For example, it doesn’t require much imagination to grasp the symbolic meaning of heart problems or brittle bones in a dream.
At the same time, one shouldn’t underestimate the possibility that the dream reflects an objective condition one is unaware of, and it might be worth consulting a doctor. However, the most common expressions of physical illness in dreams are symbolic, such as machinery not functioning properly, dirty water in the pipes, and so on.