They also offer some focus area modes that use just the one focus point you have selected or some other focus area mode that help keep things in focus in your photos.
Auto Focus Modes
Single Servo Focus
The most commonly used focus mode is Single focus. (Nikon - AF-S, Canon - One Shot AF)
Use single focus when you are making photographs of subjects that aren't moving.
When the shutter is pressed halfway the camera focuses, turns on an in-focus indicator in the viewfinder, and then locks the focus until the shutter is released, or until the shutter button is returned to it's normal position.
auto focus single mode can be used to focus, lock that focus, then move the camera slightly to recompose the framing of the shot. That way, if your camera has cross-type focus points in the middle of the focus point array, you can use the cross-type focus point to get better focus than using an outlying vertical-type focus point that is on the place you want the focus the sharpest.
Key Point - Most digital SLR's are set to the default, or you can set them up, so that if focus has not been achieved, the shutter won't release when you press the shutter release button all the way down. That is known a focus priority.
The opposite is known as shutter priority. When the camera is set to shutter priority it will release the shutter even if nothing is in focus.
Continuous Servo Focus
Use continuous focus for moving subjects. (Nikon - AF-C, Canon - AI Servo AF)
While the shutter release button is pressed halfway, the camera will continually refocus as the camera is moved to follow a moving subject. However make a note that at default settings it's possible to release the shutter when the subject is not in focus, which is known as Release priority.
Focus priority can be set, and when it is, while you are using continuous focus the camera will not release the shutter if focus has not been achieved at the chosen focus point.
Continuous focus can have some pretty slick features like predictive focus tracking. Check your Camera users manual to discover what features are available with your camera.
While the shutter release button is pressed halfway, predictive focus tracking is initiated if the subject moves towards or away from the camera and the camera tries to predict where the subject will be when the shutter is finally released.
Focus Area Modes
Single Point Area
This area mode just uses the focus point you have selected, and is intended for pretty much stationary subjects.
You select the focus point manually.
Using single servo auto focus mode with dynamic area mode, the camera just focuses on the selected single focus point.
Using continuous servo focus mode with dynamic area mode - if the subject leaves the selected focus point briefly, the camera will use information from surrounding focus points to maintain focus. In cameras having a lot of focus points, the number of surrounding focus points that are used can be selected in the camera menus. As an example - Nikon cameras having 51 focus points allow setting the number of focus points surrounding the middle of the viewfinder that are used to 9, 21, or all 51 focus points. Not all 51 focus points are cross-type focus points.
As you can probably tell, using continuous serve focus mode with dynamic area mode is a good combination for photographing action. Don't forget about also setting either focus priority or release priority in the camera.
It takes practise to get good at using continuous focus using release priority because you can release the shutter when the image is out-of-focus (OOF).