The exposition of a population to mutagenic agents (for example, the people living in the surrounds of the Chernobyl nuclear power plant and exposed to the radiation from the nuclear accident in 1986) increases the cancer incidence in that population. This occurs because the mutagenic agents increase the rate of mutation and the probability of mutant cells to proliferate in pathological manner (cancer).
Cancer itself is not a hereditarily transmissible disease. Genetic predispositions for the development of cancer, however, can be inherited.