The answer to your question depends on who was injured and what expenses you are asking about. All auto insurance policies cover medical expenses to some extent, but the amount and method of coverage varies from one insurance company or state of residence to another.
For insurance companies, the burden of protecting your health belongs on your health insurance policy. Medical expenses of your own should be addressed through a health insurance policy, except where state law requires insurance companies to use No Fault standards for insurance. Unless you live in a state which uses No Fault coverage, your car insurance will not pay for injuries to you, your spouse, or your immediate dependents. In a No Fault state, the medical expenses are addressed by each party's car insurance and the actual costs for insurers are negotiated behind the scenes in a process known as subrogation.
No matter where you live, your car insurance will pay for damages and injuries you cause to others in the course of vehicle operation. In some states, you can even be held responsible for lost wages and other expenses of the injured parties. For this reason, it is almost always a good idea to carry more liability coverage than you are required to have under state law because a single serious accident can exhaust your limits quickly. Once you exceed your insurance limits, the remaining costs are you own out of pocket responsibilities.
Your policy will clearly define what coverages are available. If you do not understand the way your policy is written or some of the information it contains, your insurance company will be happy to explain anything you do not understand. This includes such information as what constitutes a medical expense, how much expense you are covered for, and under what conditions the medical expense coverage is void, such as someone trying to hold you responsible for an unrelated preexisting condition after an accident.