The DOF preview button helps you determine what photos will look like before the image has been taken. When the button is pressed, the lens will stop down to the aperture that you have set. Then, you will be able to see a preview of what the final image will look like through the viewfinder as you would be actually seeing through the set aperture.
To understand, set the aperture at or towards the closed down aperture. Include some text in the background and focus at a nearby subject. Try this out in good natural light and on a tripod. when you press the depth of field preview button, the scene in the viewfinder will become darker but now you will be able to read the text in the background. So this give you an idea as to how much you need to close down or what aperture would be appropriate to have a good depth of field. If you do not close down the aperture, you will not be able to observe the difference.
Check out the instruction manual of your camera to find its location. Its usually in the front close to the lens. EOS 5D Mark III _EF24_105_thefront The small button next to where 77mm is written is the depth of field preview button.