A hot shot driver is basically a courier service. If you need a part delivered now, instead of shipping it through a major company, you can call a hot shot company and they will dispatch a driver / vehicle to come direct to the point of origin and then drive directly to the destination, usually as quick as right now, minimal stops. They are frequently used for urgent needs or for specialty type of items - I think agriculture equipment, industrial needs, etc.
Not sure why they are hassled in some areas more than big trucks (i seem to see a semi pulled over just about every day on my way to work), but i would guess there is a higher chance for hot shot drivers to speed, given the time sensitive nature of the loads they generally haul.