Medicare is a multi-part federal health insurance program managed by the federal government. A person applies for Medicare through the Social Security Administration, but Medicare's rules are written by another federal agency, the Centers for Medicare and Medicaid (CMS), and Medicare claims are processed by private insurance companies, called "Fiscal Intermediaries" and "Medicare Carriers," that vary from state to state.
People who have Medicare coverage may also qualify for Medicaid. When they do, Medicaid pays for their Medicare premiums, deductibles, and co-payments - as well as for many health care items, such as dental care.
Information from the U.S. Government on Medicare can be found by visiting this link.