Chris
those synchros act sort of like a brake, or more to the point a speed equalizer. When you select a gear and the collar slides towards the teeth on that gear it must first encounter the synchro ring, the inside shape (usually tapered) grabs the boss on the next gear as you push them together. Since the sliding collar has engaged the synchro first they are moving at the same speed, and the pressure going into the next gear brings the whole assembly into equal RPM. When you go into nuetral the synchro theoritically floats, if you are in any part still engaged in that synchro it will wear fast. Most are a bronze alloy. I would check the dogs that position the synchro, and usually there are spring loaded rings under the dogs to keep everything in place (either in gear or neutral). The dogs form a detent when the collar slides over the gear selected. Sounds complicated but it actually works quite well.
Hope this helps
Phil