What is the difference between a medicare participating provider and nonparticipating?

Like most things involving the government, it's kind of complicated, but basically:

A participating provider has agreed to submit all claims to the Medicare program. A non-participating provider may choose to submit, or not to submit, claims to Medicare on a case-by-case basis.

The biggest practical difference to a patient covered by Medicare is that if they go to a participating provider they will probably only be asked to cover the Medicare co-payment at the time of service. If they go to a non-participating provider, they may be asked to make payment in full at the time of service.