In cancer, why do cells duplicate themselves?
This article covers some of the key issues of cancer in layman's terms.
Essential, cancer is caused by multiple mutations in key regulatory genes which function in maintaining the cell cycle. This provokes uncontrollably rapid cell division, with only furthers the problem with genetic mutation. Here are some quotes from the article to strengthen your understanding in cancer cell mutations.

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The cells become progressively more abnormal as more genes become damaged. Often, the genes that are in control of DNA repair become damaged themselves, rendering the cells even more susceptible to ever-increasing levels of genetic mayhem.
[...] Most cancers are thought to arise from a single mutant precursor cell. As that cell divides, the resulting 'daughter' cells may acquire different mutations and different behaviors over a period of time. Those cells that gain an advantage in division or resistance to cell death will tend to take over the population. In this way, the tumor cells are able to gain a wide range of capabilities that are not normally seen in the healthy version of the cell type represented.
[...] Mutations in key regulatory genes (tumor suppressors and proto-oncogenes) alter the behavior of cells and can potentially lead to the unregulated growth seen in cancer.