The drive belt runs between the engine crankshaft and a pulley on the top of the gearbox. Access is gained by removing the plastic belt cover under the deck.
The 'spare' piece you mention is part of the belt tensioner mechanism. It will have become loose and fallen off when tension on the belt was lost (when the original broke or whatever). The bar is inserted through a hole in the back of the mower, and hooks into a hole in the gearbox casing. The length of the bar is controlled by the locknut - this pivots the gearbox and tentions the belt.
phil_saunders(a)bigfoot.com
Phil Saunders
July 2009