What is Medicare-for-all and how does it work?
Medicare for all describes a general concept of a single payer healthcare system. Right now the US has a multi-payer healthcare system, that means people pay different insurance companies but have a choice in healthcare providers. With single payer, there is one insurer, but you keep the choice in providers. Also, as the "for-all" part implies, every citizen would have access to Medicare-for-all.
Substantially all highly developed countries have a single payer universal healthcare system, many of those countries call it "Medicare." The US greatly influenced global healthcare reform in 1900s, even though it itself never passed a national Medicare plan or universal healthcare plan. Still the name "Medicare" was used by many countries.
With all the above noted, there are many different versions of national Medicare or more generally universal national healthcare systems where everyone is covered. Some systems get rid of out-of-pocket costs and handle premiums as a tax, others allow you to pay for higher tier plans. Meanwhile, some systems also use public healthcare delivery (public hospitals and doctors).
Although Medicare-for-all can works lots of ways, the basic idea is that everyone is covered under public insurance plans, and this is used to keep costs down and expand coverage. From there it is a matter of how the system choses to share costs between the public and private parts of the healthcare sector.
Learn more about single payer.