Try it on a close object. Focus on it. Set the aperture to about f4 or f5.6, then depress the DOF button. You should see the aperture close down to that size (works better if you have a f2.8 or faster lens to try) There you should be able to see the focus zone clear only, the rest of the pic is blurred.
Try it again with a smaller aperture (say f8 or f9) then you should see a even dimmer picture. But more of the picture will be clearer now. That's a larger DOF zone now.
Normally, when you look thru the viewfinder, it is bright because the aperature is at the max size... When you press the Depth of Field preview button, the aperature close down to the aperature size you set on your camera... Since the aperature size decrease, less light enters implies darker...
The use of this button is to preview the DOF first before you shoot so that the things you want to include will not be in bokeh... (blurred out)