First, let's review the three things that directly influence how all photos are captured on both film and digital cameras:

1) Aperture: the lens opening
2) Shutter Speed: the speed of opening and closing the shutter, which determines how long the subject matter stays on the film that comes through the given aperture
3) The speed of the film (a.k.a. ISO setting), which directly influences what choices of aperture and shutter speeds you can use

ISO Setting
Before your camera can detect aperture and shutter speed for a particular subject, it must be told how many worker bees are loaded into the camera (i.e. the film and its corresponding ISO). The more worker bees there are, the less time they need to capture the same amount of light, so the ISO setting directly impacts the aperture and shutter speed settings.

These days, ISO on film cameras is detected by a bar code on the film's cassette, which the camera reads and then tells the light meter. On digital cameras, you can set the ISO to a particular rating by selecting it in the menu, or leave it on the automatic setting so that the camera decides which ISO speed to use. Once your camera knows how many worker bees it has, it will be able to detect which aperture and shutter speeds are ideal for various conditions.

Aperture
Aperture controls the volume of light that passes through the lens and onto the film. The volume of light is determined by the size of the lens opening (the aperture): big, medium, or small openings. Aperture works in conjunction with Shutter Speed to correctly expose an image. Depending on the lighting conditions (night vs overcast vs sunny), a given aperture will require a different partner shutter speed.

Most cameras recommend these settings automatically for you, assuming you want everything in the photo to be in focus. You can usually opt to set the aperture and have the camera pick an appropriate shutter speed (called aperture-priority), or vice versa (called shutter speed-priority). If ever you want to change the depth of field (i.e. what's in focus), the aperture-priority setting will come in handy, if not full manual where you set both aperture and shutter speed.

Depth of Field
The term 'Depth of field' simply refers to a picture's overall sharpness. It is the direct result of the aperture setting on your camera. By setting the aperture (a.k.a f-stop) to a small numbere.g. f/2.8you are setting the lens opening to be large. Such a 'wide-open' aperture limits the plane or field of focus to be very narrow: this is called a small or narrow depth of field. For example, if you're photographing a long line of fuzzy ducks extending into the distance, and you only want one duck in the middle to be in focus, then you would open up your aperture by setting it to a small number, such as f/2.8. Once you've chosen this setting, your camera will help you figure out the appropriate shutter speed to provide a good overall exposure.

By setting the aperture to a large numbere.g. f/16, f/22 or even f/32you are setting the lens opening to be very small: this is called a large depth of field. This small aperture allows the camera to focus clearly on things both close and far in the same shot. Continuing on with our fuzzy duck example, using a small aperture will allow you to capture the entire row of ducks in perfect focus. The near duck will be just as sharp as the far duck, as will all the ducks in the middle.

Try it out! Once you've focused on a subject, you will notice that there are areas beyond and/or in front of what you focused on that are not sharp. Assuming you want everything sharp, the laws of depth of field say to use a small aperture of f/16, f/22, or f/32. If you instead want a narrow field of sharpness in your image, the laws of depth of field say to use a wide-open aperture of f/2.8 or f/3.5.

In a nutshell, those big aperture numbers - f/16, f/22, f/32render the greatest depth of field or area of overall sharpness and those smaller aperture numbersf/2.8, f/4, f/5.6render a minimal area of sharpness beyond or in front of what you have chosen to focus on. Again, depending on lighting conditions, different shutter speeds will be required to expose the image correctly.

Caveat for digital photographers:
These depth of field rules and example f-stops were created for those using 35mm format cameras, and you will find reference to them all over books and the internet. Digital cameras are typically closer to 38mm format, and will thus have better results narrowing their aperture (so as to get everything in focus). The claim to fame of digital cameras is to have excellent focus from near to far - infinity and beyond, but in doing so have limited ability to capture narrow focus. For example, f/2.8 on a typical digital camera will not be a large enough aperture to narrow your depth of field sufficiently to only get one fuzzy duck in focus. DSLR owners can simply purchase a macro lens to do this, but digital point & shoot owners may not have the capability to narrow their depth of field noticeably. Best to stick to landscape shots!