the very much simplified way of explaining it is that it smooths out the peaks of the wave.
it does depend on the settings of the shaper and the wave going in to it though.
if you look at a waveshaper with a spline graph it is easier to explain. this one isnt a sine, in fact it will do nothing to the sound, but ill use it as an example:
the X axis is the signal gain going in and the Y axis is the signal coming out. so when the audio going in is at +1 (X=+1), if that point on the graph is at +0.5 on the Y axis then any signal hitting +1 will come out the other side at +0.5.
now if you imagine a sine shape on there (which would look how the below GIF starts, sorry it was the best i could find), you would be adding a small amount of gain at +/-0.5 and none (practically) at 0 or +/-1, with a smooth curve between those points. make sense?