A procession of mimes walking through the streets of your town would be surprising and somewhat terrifying. A line or group of people moving together in a deliberate way is a procession.
You're most likely to see a procession during some kind of ceremony, parade, or festival. A line of cars moving together to a cemetery is a funeral procession, and a bunch of parents pushing babies in strollers in a parade are also a procession. Another meaning of procession is any line or succession of people moving continuously, like a procession of local politicians knocking on your door one afternoon. The root of procession is the Latin processio, "marching forward."