The sheave is spring loaded just like most idlers that automatically keeps belts tensioned. As shifter is moved to higher speeds it allows the Brake/Clutch to rotate more from the depress position. This in turn via linkages from the brake/clutch pedal allows the very large spring to pull the sheave assembly rearwards along its rotating axis thus applying more tension on the engine to sheave belt which forces the sheave to slide closing the gap that the rear belt has to ride in. This forces to belt outwards effectively acting like a larger pulley is now there. The idler on the rear belt gives. As you brake/clutch or shift to a lower speed the idler takes up the slack as the sheave returns to normal position.
The slots are there so as you depress the brake/clutch you don't need move the shifter everytime you stop. The shifter just provides a positive stop to the pedal when you release it.
Hopefully I haven't confused you too much here as I don't have manual that details this particular setup which is I believe the MTD 600 series. Even in that series there several variations of the system.
If your planning changing the engine pulley to a different all bets are off as which size belt you need. It would take experimentation from there.
