When a person or a group monitors a specific area, that's a patrol. A police officer's night patrol might involve walking a beat on certain city streets.
A patrol is the activity of watching a neighborhood or region, and also refers to the person or group doing the watching. And when you join such a group, you can say you patrol. Your neighborhood watch group might patrol the town in groups of three, driving up and down the streets keeping an eye out for suspicious activity. The French patrouille, "a night watch," comes from patrouiller, "go the rounds," and originally "tramp trough the mud."