for information
http://en.wikipedia.org/wiki/Manual_transmission
Synchronized transmission
Most modern cars are fitted with a synchronized gear box. Transmission gears are always in mesh and rotating, but gears on one shaft can freely rotate or be locked to the shaft. The locking mechanism for a gear consists of a collar (or dog collar) on the shaft which is able to slide sideways so that teeth (or dogs) on its inner surface bridge two circular rings with teeth on their outer circumference: one attached to the gear, one to the shaft. When the rings are bridged by the collar, that particular gear is rotationally locked to the shaft and determines the output speed of the transmission. The gearshift lever manipulates the collars using a set of linkages, so arranged so that one collar may be permitted to lock only one gear at any one time; when "shifting gears," the locking collar from one gear is disengaged before that of another engaged. One collar often serves for two gears; sliding in one direction selects one transmission speed, in the other direction selects another.
In a synchromesh gearbox, to correctly match the speed of the gear to that of the shaft as the gear is engaged, the collar initially applies a force to a cone-shaped brass clutch (I believe this is what has worn in your box) attached to the gear, which brings the speeds to match prior to the collar locking into place. The collar is prevented from bridging the locking rings when the speeds are mismatched by synchro rings (also called blocker rings or baulk rings, with the latter being spelled balk in the U.S.). The synchro ring rotates slightly due to the frictional torque from the cone clutch. In this position, the dog clutch is prevented from engaging. The brass clutch ring gradually causes parts to spin at the same speed. When they do spin the same speed, there is no more torque from the cone clutch, and the dog clutch is allowed to fall in to engagement. In a modern gearbox, the action of all of these components is so smooth and fast it is hardly noticed.