Hopefully, this explanation will be helpful:
Most cells that go through mitosis are able to halt themselves from continuing when they make contact with other like cells. This is known as "contact inhibition" Cancerous cells do not have this function, allowing them to divide rapidly.
Chemotherapy, depending on the set of cells, has the ability to slow down mitosis. It works more effectively the more rapidly the cells are dividing, but it does not know the difference between cancerous and healthy cells.
Chemotherapy kills these cells off through cell-cycle specific means, in which it only works during cell division.
