How can disruptions to the cell cycle lead to tumors and cancer?
When a cell divides, it copies its DNA. When it does that, there can be an alteration in the DNA sequence that changes the behaviour of the cell. That is called a mutation. You have mutations in your body all the time, but they are not usually significant.
Cancer is when one cell has gotten a specific mutation that makes it so that the cell and its duplicates cannot stop duplicating.