Camera Aperture is quite simply a hole. It is an adjustable hole. The adjustments are normally 1 stop increments. For example f/2.8 is double the size of f/5.6. Because the aperture is double the size, it lets twice as much light onto the sensor. This can result in a brighter image (1 stop brighter) or a faster shutter speed to achieve the same brightness. The shutter speed would be twice as fast (1 stop) in this case.
Why would I pick f/2.8 over f/5.6?
Choosing f/2.8 will help you in a low light situation when you have to hold the camera by hand. The shutter will be twice as fast as the f/5.6.
Shooting this cat portrait at f/2.8 is not so much about reducing the shutter speed as creating a shallow Depth of Field (DOF). The eyes are in focus (focal plane), but the detail starts to get blurred on his nose (in front of the focal plane) and even more on his right ear (behind the focal plane). The Depth of field just about covers his face. This can be desirable for a number of reasons. It gives the images a sense of depth and it draws the viewers attention to the important part of the portrait – the eyes. Because of the blur on his right ear, you can sense that his left ear is slightly forward.
Why would I shoot with small apertures like f/22?
The smaller apertures let in less light which means slower shutter speeds, so they typically require a tripod to work with successfully. The desired effect is that everything in the image appears sharp. There is little or no blur because the DOF covers all objects. This is desirable in a Landscape photograph. As a trade off, nothing is really sharp at f/22, it is to do with being so far from the lens sweet spot (best aperture – with many lenses this is around f/8). Most landscape photographers will actually use f/11-16 and achieve a good DOF. They achieve better sharpness because they are closer to the sweet spot. Some photographers will choose f/22 simply for the slower shutter speed if they want to blur water like a silky waterfall effect. While this is effective, the correct choice would be a Neutral Density (dark) filter and the correct aperture choice regarding DOF.
For a more advanced discussion see my Arguing for Aperture article.
Aperture choice can be useful to manipulate the shutter speed. Aperture works with ISO and shutter speed to form the exposure triangle. But really your choice of aperture should be a consideration of DOF. DOF is an important key to communicating Depth and for guiding attention through an image.
But… aperture is not the only choice that affects DOF. Focal length (how wide is your lens) affects aperture. A wide angle lens will naturally have a large DOF whereas a long lens will naturally have a shallow DOF. Technically, DOF is the same in both, but it is the distance of the lens to the subject that will contribute to the shape of the DOF.