Neither Hazel nor Augustus has control over their cancer. Despite all the research and treatments, there is no guaranteed way to prevent and eradicate cancer. Fate seems to control whether a person is healthy or sick.
The phrase "an imperial affliction" means "suffering sent by a higher power." The title of Peter Van Houten's book (which plays an important role in Hazel and Gus's lives) emphasizes the inability of humans to escape suffering.
The characters seem to agree with the Greek idea that one's destiny is shaped by the stars. Hazel says she and Augustus are "star-crossed lovers" and Van Houten writes that the "fault [is] in our stars".
Gus's cigarettes are a way for him to metaphorically control his own fate. The unlit cigarettes allow him to play with death without dying as a result. They give him confidence, but don't change the reality that he has no control over his death.