One of the more difficult parts of a cancer diagnosis is hair loss. Depending on what kid of chemotherapy regimen a patient undergoes, and the severity of the disease, some patients will keep their hair, but many patients lose it. It has to do with how cancer works. When cells grow and divide normally, a process called mitosis, it's all good. When cancer happens, cells go into overdrive, replicating and spreading the disease into tumors, sometimes even moving to other parts of the body via the bloodstream or lymphatic system. The goal of chemotherapy is to shut down the rampant mitosis, but many of the regularly used drugs shut down all cell growth, not just the cancerous cells.
Hair cells are naturally pretty fast at dividing, since the hair is constantly growing. Chemo drugs act on these cells, and other fast dividing cells and the result is that new hair growth is shut down and eventually the hair is starved of new cells and falls out. Once the medication is stopped however, the cells are back at it and most of the time hair is regrown. While hair loss and other side effects from chemo are a drag, if the end result is good health, then it's a fair trade.