The nuts are tightened to hold the stationary inner bushes of the pulleys, tightly against the ends of the square part in the center of the clutch shaft. The inner bush is circled in red in this picture of aldot's:
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Clamping the inner bushes in that way ensures that they are effectively locked to the shaft, and rotate with it. The pulleys rotate on the bushes when the clutches are disengaged, or rotate with the bushes when the clutches are engaged. Hence you tighten those nuts quite firmly, recognising the diameter of the threads involved. I'd probably use about 25 lb ft.

The shims set the clearance between the pulleys (driven by the engine) and the clutch disks (which can only rotate if the clutch shaft rotates. If the disks rotate, so does the chain drive to the rear wheels). The clutch disks slide freely along the square part of the clutch shaft, but are held away from the pulleys by compression springs in between:
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You can see the spring in the red circle. The bush seems to have been removed from the center of the pulley in this picture (also from aldot, like the previous one).

The thrust bearing in the center of the shaft, between the clutch disks, is also free to slide along the square shaft in either direction, when pushed by the clutch linkage.