A single payer healthcare system is exactly what it sounds like -- healthcare is paid for by only one entity. In all cases across the world where a single payer system has been implemented, that payer is the government.
In conversations about healthcare reform, people often confuse a single payer system with universal healthcare, which instead refers to the fact that every citizen in that system has access to basic healthcare. Universal systems may be a combination of private and publicly funded care.
In the United States, Medicare is a single payer system for people age 65 and older. Those who favor a single payer system suggest it would look like Medicare for everyone. They also cite the fact that the total administrative cost for Medicare services is only 3%, whereas private insurance administrative costs may amount to 25% or more.
Most Americans are surprised to learn that many physicians in the United States support a single payer system. In fact, more than 15,000 doctors support an organization called Physicians for a National Health Plan (PNHP) which has actively pursued a single payer system for many years.
The biggest reason these physicians support a single payer system is because the billing aspects of their practices often cost more than the rest of their practice. It's not unusual for a doctor to devote more staff, therefore more expense, to billing than to patient care.
Most opposition to a single-payer system comes from the health insurance companies that would no longer provide the services they now offer, which means to them a reduction in revenue streams and profits.