The term "Single-payer" means that one fund, administered by a non-profit government agency accountable to the public would make payment for all medical services. Period. The hundreds of private health insurance companies that currently do this work—each raking in profits for its stockholders and each with its own expensive bureaucracy and complicated policies—would no longer be involved as middle men. The choice of doctors and hospitals would be yours and decisions about your care would be made by you and your doctor, not an insurance company executive interested only in the bottom line. Medicare is one example of a single-payer plan.
For an entertaining and informative overview of single-payer, take a look at "WHAT IS SINGLE-PAYER?" an animation created for the general public by Stanford University Medical Student Graham Walker.
Like music with your messages? "PIRATES OF THE HEALTH CARE-IBBEAN," an animation with music by the Austin Lounge Lizards, will tickle your funnybone.