The posse program is kind of unique to AZ and other western states I think. Maricopa County makes liberal use of it. Under the AZ Constitution, a county sheriff can call upon any citizen to assist them (think old west stuff). When this is done, the citizen has police powers for that specific task as directed. The posse formalizes that. We go through an application process including criminal history, fingerprints, etc. We wear the same uniform as a deputy, except the badge says posse instead of deputy sheriff. We are civilians, but when directed by a sworn deputy sheriff, we have the same authority as a peace officer by law only for the activity authorized at that time. Off duty we have no peace officer status or authority. MCSO also has reserve deputies that are full authority peace officers.
MCSO has established a training program that allows us to carry OC, handcuffs, baton, Taser, and even firearms if we can shoot the same course of fire as a peace officer with a passing score.
Possemen assist deputies by riding as a second man in a unit, doing prisoner transports, traffic control, etc.
My unit, medical rescue, assists deputies in the Lake Patrol division of MCSO, on the chain of lakes outside Phoenix created by the damming of the Salt River. We provide EMS first response as well since fire dept response times are extended in the area, from 15 mins to 1 hour depending on location.
Hope that helps clarify.