Cancer is so awful, but I really don't know how it works or why its so hard to cure.
Cancer is kind of an umbrella term for a group of diseases that involve abnormal cell growth. The cells go out of control and invade the other parts of the body. 
Ohh so is it just hard to near impossible to stop the intrusive cell growth?
If you remove one tumor, there's the chance another one will grow somewhere else. Benign tumors, in contrast, don't spread. They're easily removed and treated. 
Damn that's insane. So how does chemo work? Does the radiation slow or stop the growth of these cells?
Chemotherapy may be given with the intent of curing the cancer, usually with lots of other drugs, but it also can just be to prolong life or make symptoms less severe. 
That's so sad that we haven't found a cure for such a terrible disease, especially with how the best course of action is very harmful to the body anyway.
It's true, especially since current estimates suggest 2 in 5 people will have cancer at some point in their lifetime. But there are also lots of experimental treatments in development!