Automatic
This mode is self explanatory—it does everything for you. This is for point-and-click photographers—but, if you are reading this then odds are automatic mode is not you.
Semi-Automatic
While the name of this mode conjures up mental imagery of bad-ass machine guns, it is not quite that exciting. A semi-automatic mode is perfect for beginner to intermediate photographers who have not yet learned how to control the shutter, aperture, ISO, white balance, and other manual tools. With semi-automatic there are three different sub-modes: aperture priority mode (A or AV), Shutter Priority Mode (S or TV) and Program Mode (P)
Aperture Priority (A or AV)
This mode simply implies that while all the other elements will be taken care of for you via the automatic setting, you are creating a manual priority on the aperture. This allows you to control the depth of field, which is generally used for stationary subjects where the shutter speed isn’t a factor. When using this setting the larger aperture number you use the more of the background will be in focus.
Shutter Priority (S or TV)
Shutter priority means that you are telling the camera to auto-choose the other settings (ISO, white balance, aperture, etc) while focusing on the speed of the shutter. This mode is generally used for action photos where you want to control the exposure and focus of freeze-frame images. You can also use this mode to create blurred action photos.
It can also help you control the light in your photos, for example using a slow shutter speed can help increase the light captured in your photo.
Program (P)
Not all cameras have this mode, as many use solely a fully automatic mode, but if your camera has the program mode you can use it to control some of the manual features whilst still making use of auto-intelligence. The program mode gives you a little more control over flash, white balance and ISO—but without needing the know-how about how to use them completely manually.
Fully Manual
Working in a fully manual mode means you have control over every aspect of your image, including flash, white balance, shutter speed, aperture and ISO. Moving from semi-automatic can be difficult as it requires higher levels of thinking.
The flexibility is the greatest though in program mode as it essentially encapsulates all the modes listed above into one. Once you have mastered all the other modes moving to this one will be easier. This mode is best used in situations where the camera cannot decide on its own which settings to use—when the photos come out over- or under-exposed, out of focus, focused on the wrong items, etc.
Manual mode can also ensure consistency—an important aspect if you are completing a project and require a similarity between photos.