In cancer, this tightly regulated process breaks down and cancer cells grow beyond where a normal cell would stop growing. Cancer cells invade nearby tissue or they invade the blood stream and travel to other parts of the body. They don't obey the normal mechanisms that either turn on or turn off cell growth.
Why are cancer cells so resistant?
The following analogy for the blood system helps to answer that question. You have a series of very, very young cells called "stem cells", which are like infants. They mature over a certain period of time and become functional adults - red cells, platelets, white cells. Normally, around half of these stem cells are committed to maturing into the adult cells. The other half remain as infants and either sleep in a resting phase, or divide and create more infant stem cells.
Many cancers seem to start because of mutations that occur in these long-lived stem cells. Nature has already perfected the means of keeping these particular cells alive for decades. Thus, it's tough to cure most cancers because they tend to develop in this subpopulation of very resistant cells.
How do these new, targeted drugs work to fight cancer?
The mutations that produce either abnormal enzymes or cell receptors that drive cancer cells are different in different types of cancer, and some mutations are very unique. The targeted drugs are designed to identify the particular mutation and its product, and inhibit those cells that contain the mutation.
By "inhibiting", do you mean that the drug kills the cancer cells?
Some of these targeted drugs kill the cells. Some just inhibit cell growth or spread. They decrease the size of a tumor without necessarily eliminating it.