Medicare Advantage (formerly Medicare + Choice) is a program through which the Medicare population can receive benefits with a private insurance plan.
The government pays insurers a set amount to cover a portion of the plan while insurers can offer a variety of other benefits (and some other costs) according to rules set down by the Center for Medicare and Medicaid Solutions.
In many cases, prescription drug coverage (Medicare Part D) is included in Medicare Advantage plans.
Types of Plans

• Preferred Provider Organization (PPO): Some Medicare Advantage plans contract with a network of health care providers (e.
  g.
  hospitals, doctors) and charge less when participants use services from those providers.
  Plan participants can use outside providers for an additional cost.
  
• Health Management Organization (HMO): HMOs also have a network of pre-approved service providers that will be covered within your plan, however the one main difference is that you must elect a primary care physician.
  This primary care physician acts as your personal doctor, but also as your health care coordinator.
  If you ever needed to see a specialty doctor who was not in your HMO plan network, your primary care physician could offer you a referral if they deemed it necessary.
  With this referral, your insurance will cover a share of the costs but without it you can expect to pay full price.
  
• Private Fee-for-Service (PFFS): PFFS plans act much like traditional Medicare in that you can see any care provider that will accept your plan's payment arrangements.
  Sometimes these plans set up networks of providers for certain categories of services but allow you to see anyone ouside the network who will accept the plan's payment.
  
• Special Needs Plan (SNP): Special Needs Plans are available for members of the Medicare-eligible population who are also eligible for Medicaid, are institutionalized or are afflicted with a chronic condition.
  
• Medical Savings Accounts (MSA): Medical Savings Accounts usually do not require a premium as they have a high deductible.
  Participants must pay the Medicare Part B premium, and also pay for Medicare covered services, and after a participant reaches the deductible, the plan will pay for Medicare services.
  Medicare also deposits money in a savings account to pay for Medical costs.
  MSA plans do not include prescription drugs but a standalone Prescription Drug Plan can often be purchased.
  

Medicare Advantage is beneficial because it usually doesn't require the purchase of a Medicare Supplement Plan and usually offers additional benefits such as dental and vision coverage or "wellness" benefits such as discounted gym memberships.
Participants who opt to enroll in Medicare Advantage retain all the protections of regular Medicare patients and retain the right to petition the Center for Medicare and Medicaid Services.