What does an overdose of drugs do to you?

It really depends on what drug you overdose on. When you overdose (depending no the route of administration such as ingestion, injection, or inhalation), the body processes the drug differently.
So a ingested drug can damage your esophagus and stomach. Some drugs damage your liver as the liver is the primary site for drug metabolism in the body. Complete liver failure can occur and other drugs injure the pancreas. Once the drug is in the blood stream, high levels will result in the drug being distributed to all areas of the body, resulting in side effects throughout the body's organ systems. High blood levels of a drug lets that drug penetrate into the brain causing decreased alertness, brain activity and even coma. As your body attempts to filter the drug out of the body, it can damage the nephrons of the kidney and leave you in a catabolic state.

Essentially, a drug overdose does not kill you right away. It will primarily damage various organ systems the drug uses to get into the body as the body uses various mechanisms to compensate for the drug's effects to protect you. If you are getting medical help, you will most likely live but will lead a life that is dependent on heavy medications, organ transplant, disability, or hospitalization.