It scales the deflected shape, so that you can actually see them.
Assuming you are designing in steel, and your structure is about 1 metre long, say, then your flexural and axial deflections are likely to be of the order of only 2 or 3 mm, say. If you plot the deflections with a Scale Factor of 1.0, you probably won't see the deformed shape at all. (Unless your whole structure is mounted on soft springs, but even then, you would only see the spring deflection, NOT the flexural and axial deflections.) Increase the scale to about 100, say, and the apparent deflection would increase to 200 or 300 mm, about 20% of the characteristic size of the structure – big enough to see what is really going on.
It is important to know that your deflections are correct – both in magnitude AND in general shape – because this will tell you whether your model is behaving like the real thing. If your deflections are wrong for any reason (incorrect loads, constraints, material properties, etc), then ALL of your results are suspect – element stresses, etc.
The Scale Deformations factor just exaggerates the apparent magnitude of the deflected shape, as plotted on screen. It doesn’t actually change any of the calculated deflections, or other results.
The point is that you probably can’t even see a 2 mm deflection on a 1 metre long object, let along check that it is deflecting in the right way, in the right direction, in all the right places.
By exaggerating the apparent deflections, you can easily see where the big deflections are, in which direction it is deflecting, etc. Try animating the exaggerated deflected shape – yes, it looks alarming, but just remember the ACTUAL deflections are only 1/SCALE times the apparent deflections. Now try animating the deflected shape with Deflection Scale Factor set to 1.0. True, these are the REAL deflections, but how much can you see? Probably just a little bit of wiggling, if anything.