The 737 (photo) and 727 have basically the same setup regarding the stabilizer trim wheel. Their are three basic modes of operation which I'll try to explain and how they affect the trim wheels.
The first mode operates the stab trim using yoke mounted switches (sometimes referred to as pickle switches). This moves the horizontal stabilizer using a large electric motor attached to a jackscrew which raises and lowers the stabilizer in much the same way as a nut moves up and down a bolt. This is controlled directly by the pilot with his thumb on the pickle switch. There is a long control cable run from the stabilizer all the way to below the cockpit floor (sort of a closed loop) where thru a mechanical/chain linkage it connects to the stab trim wheels in the cockpit. As the pilot controls the horizontal stabilizer up or down, the cable run moves and back drives the trim wheels. Now for arguments sake, if the pilot moves the pickle switch but the trim wheel doesn't move, rest assured the stabilizer is not moving either.
Another mode is when the autopilot is in command and moves the stabilizer (auto pitch trim). The operation mechanically is virtually the same except the auto pitch trim uses a smaller moter which moves the stabilizer at a slower rate than the motor that the crew uses via the pickle switch. When the flight crew sees the trim wheels moving in this mode, it alerts them to the fact that the autopilot is moving the stab trim.
Now the last mode I'll speak of is the manual mode. We've discussed how the stabilizer backdrives the trim wheels when the stabilizer is moved electrically with either the the pilot or autopilot commanding it. But the trim wheels in the 727/737 allow you to move the horizontal stabilizer by manually turning the trim wheels using handles that fold out of each trim wheel. By doing this, you're turning the trim wheel which in turn moves the closed loop cable system which manually turns the jackscew assembly thus raising and lowering the horizontal stabilizer. Not much effort is required to do this on the ground although in the air is probably a different story.
One caution though. If the handle is folded out of the trim wheel, don't hit the pickle switch. It really hurts getting hit in the knee or your partners knee with the handle as it swings around. Youch. I hope I didn't bore you too much.
You're only as good as your last departure.