I'll allow myself to post a link to an image (by Bill Sohne, whoever that is ). If I type crap, please correct me
The swan neck is to the right. Its pretty much a flexible metal piece, acting kind of like a spring. You can also make out the tiny screw (pointing horizontally so to say) which is turned and thus moves the regulator. The regulator is the small "lever" which controls the beat of the balance assembly - the spring is attached to it I believe. Turning the screw means the beat rate is either increased or decreased by a small amount, allowing very-fine control.
The swan neck keeps the adjustment secure, thus the movement is more reliable. Or so I've read. Panerai movements seem to employ the swan neck a lot, hence most people want movements with swan neck - its closer to the real thing after all. Lots of swan necks on asian movements seem to be decorative tho - the screw doesnt even touch the regulator..
PS I am simply writing the way I think it works, I am not really a watchsmith or movement expert or anything.. so correct me if I'm wrong