I recently did a silly little test that every photography book tells you to do as practice, but for some reason I had never done. The test is to show the effect of aperture on depth-of-field. The more open the lens (smaller f-stop), the shallower the depth of field is and conversely, the smaller the lens opening, the larger the depth-of-field. Also focal length plays into the equation. Here is a simple calculator that shows you the depth-of-field for a certain f-stop/focal length combination. Strange that I never actually did it as I use the effect all the time in my photography to for example isolate people from their backgrounds. It is the number one thing that makes people think you are a professional, so it is a good idea to know how to use it. Here is an example of a prime Nikkor 50 mm/1.8 lens on a DX Nikon DSLR:
As you see, the depth-of-field is extremely narrow and does not even extend throughout one leaf.
At 2.8 the depth-of-field is much less narrow and several leafs are in focus.
At 5.6 most of the field is in focus, but the extremes are still blurry.
And finally, f/11
Basically everything is in focus. If you go much further on a small sensor (DX) DSLR, you will loose resolution due to diffraction. In the last image, at f/22 this is the case, but fortunately, you will never see this at websizes, you will even have trouble seeing it in largish prints.
Again, simple, but I thought an effective demonstration.
Lastly, a demonstration of the effect in a simple portrait:
Bride getting ready:
As you can see only her right eye is in focus. Her left eye is already out.