What do chemotherapy drugs do to your body?

Many things. Chemotherapy kills cells that rapidly divide. These include hair cells and cells lining your stomach, intestines and mouth, and blood cells. Different chemotherapies have different side effects, but many cause hair loss, diarrhea and indigestion, mouth sores and decreased blood counts. Some cause heart damage, hearing loss, or nerve damage.
Different effects. Chemotherapy is a very broad term used to refer to a large number of drugs that treat cancer. They have very different effects and side effects. Some cause hair loss; others don't. Some are potentially toxic to the heart, lungs, or nerves--this is why they're prescribed by doctors (oncologists) who are cancer experts and watch the doses closely. It depends what kind of cancer needs treatment.