Medicare Benefits. Medicare is our country’s health insurance program for people age 65 or older. Certain people younger than age 65 can qualify for Medicare, too, including those who have disabilities and those who have permanent kidney failure.The program helps with the cost of health care, but it does not cover all medical expenses or the cost of most long-term care.More...ertain people younger than age 65 can qualify for Medicare, too, including those who have disabilities and those who have permanent kidney failure. The program helps with the cost of health care, but it does not cover all medical expenses or the cost of most long-term care. More...