If you do nothing else, please click on the link in the very last sentence of this article for a great video of what your camera settings do.
Each camera has its own unique capabilities and settings. This article will attempt to describe the basic features of a camera in simple terms.
Auto setting - Usually this setting is exactly as its name implies, automatic. Based on the ISO (digital/film speed) setting the camera will use its light reading capabilities and set the shutter speed and aperture (f-stop) setting according to its light reading and if the camera thinks it needs additional light the camera will activate its built-in or pop-up flash.
The concern with the "auto" setting is that some cameras the ISO settings will change as the camera needs more light to reach its sensor. Having a higher ISO keeps the shutter fast enough or the aperture open enough not to blur the photograph during the picture taking process. Obviously not having your camera correctly focused will cause the image to be blurred also.
A high ISO with inexpensive and cheaper digital sensors inside will cause grain and/or may blur your photograph. Camera manufacturers have continued to produce better sensors as time goes on, however a 1600 ISO rating in a less expensive camera will not give the same quality photograph as a top of the line professional camera such as a Nikon D-700, D3 or a D3x just to name a few.
The bottom line is, you get what you pay for. Most people do not have a need for the higher end cameras for their everyday home family or vacation pictures. Just be aware your cheaper sensors can cause the problems above and be able to recognize what may be causing the grain and/or blur. Most people will do just fine with the everyday inexpensive cameras.
The "P" setting is usually the same setting as the "Auto" setting except the on-board flash has to be manually popped up.
The "A" setting is the aperture/f-stop setting and determines the amount of light the lens lets in the camera's sensor or film. It also has to do with the "dept of field."
First let's address the aperture setting in very simple terms. The smaller the size of the opening of the aperture the sharper the picture will be. The size of the openings are usually indicated by these settings f-45, f-32, f22, f-16, f-8, f-5.6, f4, f3.5, f-2.8, f-2.0, f-1.5 and f-1-2 as an example. The F-45 setting/opening would be very small and let in the least amount of light and make the picture very sharp and have a great amount of dept of field meaning that items from 5 feet to infinity might be in focus. Think of it like this, remember when you take an eye examine and squint your eyes by closing your eyelids somewhat and you think you could see clearer? Well when the aperture is stopped down (small opening) it really does see clearer.
Now on the other end a f-1.2 opening lets in a lot of light, lets the shutter setting be faster and the ISO setting lower. Based on the quality of your lens the picture will still be sharp but only for a short distance. Depending on how close you are to what is in focus the dept of field may only be inches.
F-45 and f-1-2 are the extremes, but most camera lens will be from f-22 to a f-3.5. The more light the lens lets in such as an f1.2 lens the more it will cost.
"S" is the shutter speed of the camera. The slower the shutter speed the more chance of camera shake. Most people can not handhold a normal focal length lens (35-50mm) under a 30th of a second. For the normal person I'd try to be sure the shutter speed was at least a 60th of a second.
"M" is the manual mode where you set the shutter and aperture yourself.
For more excellent information about the settings on the camera, a must see...