What exactly is Medicare? It's a federal health insurance program for: People 65 years of age or over People with a disability People under age 65 with certain disabilities, and people of all ages with End-Stage Renal Disease (permanent kidney failure requiring dialysis or kidney transplant. Medicare Part A: Hospital Insurance - Most people don't pay a premium for Part A because they or a spouse already paid for it through their payroll taxes while working. Medicare Part A (H