Why does the lawn mower blade not turn?

If you have a belt driven blade set up either the belt has jammed the pulley because it is worn out or the belt is broken. It could also be that there is a problem with the pulley's, but this is rare.

I agree that the belt is the most likely problem. But there may also be a problem with the cable or linkage that engages the belt. If your belt looks good then have someone try to engage them with the mower not running and see if everything looks like it is moving properly to stretch the belt and engage it.

If this is a push mower then the spline on the blade or crankshaft is probably stripped.