Imagine you have two kids, one named "Fee", and the other named "Value". One weekend, you tell Fee and Value to each build identical treehouses, one on each of the two trees in your backyard. Your kids ask how you'll pay for them and you tell Fee that he can bring you receipts for materials and tools he purchases from the nearby hardware store and, if you think they're reasonable, you'll pay him back. Value get reimbursed differently. You give him $50 and tell him to spend it however he wants as long as he builds the treehouse. If he spends less than $50, he can keep the difference.
This example roughly illustrates the difference between fee-based and value based plans in health care. In the former, providers (such as doctors and hospitals) are reimbursed by Medicare for each service they perform. Medicare actually has a list of how much they'll reimburse for each medical procedure that could possibly be administered to you. This is how Original Medicare and Medigap coverage work.
Medicare Advantage (MA) plans are value-based. The government gives MA carriers a fixed amount of money per person they insure. This is called a capitation fee, after the word "capita", referring to "per head". The plans can spend this money however they want as long as their members have quality health outcomes. One way MA plans do this is by taking more control of what services you can use and when. For example, unlike Medigap plans or Original Medicare, MA plans require you to see in-network doctors rather than any doctor you like. Many also require your primary physician to refer you to a specialist. You can't go straight to one.
The value based nature of Medicare Advantage plans allows some of them to be zero premium. Some of them even pay part of your Part B premium. This can be appealing to folks looking to save money today, but remember that insurance is all about paying less today to decrease the chances of paying a lot more tomorrow.

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