Well, when the engine is idling, the spark should be occurring just before top dead center. This is the timing you set when the engine is off and you're doing the dance with points gap, advancer plate, test light and tick marks on the alternator rotor.
The spark doesn't occur exactly AT TDC because if it did, by the time the fuel-air mixture burned to the point of doing work on the piston, the piston would be already partway down the cylinder, negating some of the work done by the expanding gases.
As the engine rpm increases, the spark needs to occur earlier and earlier before top dead center for the reason as described above. However, if the spark occurs TOO early, the expanding, burning gases conflict with the still-rising piston on the compression stroke. This conflict is engine knocking.
The mechanical advance uses centrifugal force to slightly 'advance' the points cam as rpm increases. This causes the points to open earlier and earlier as rpm increases. The amount of this advance follows a 'curve' dictated by the amount those weights move outward. Eventually, the weights are fully outward (against the stops on the advancer mechanism), and the spark is advanced as much as it's going to. The advance is "all in". The starting rpm of weight movement and the final "all in" rpm are determined by the strength of the springs. Stronger springs will delay the advance movement and require more rpm to fully advance. Weaker springs have the opposite effect - the advance will be all in at too low an rpm.
If the spark is not advanced enough, the engine doesn't produce as much power as it might (because the combustion isn't occurring soon enough). If the spark is too advanced, you get the engine knock (which can be destructive to pistons, rods, etc).
I think that about sums it up...