With manual focus, the camera stays out of the focus equation and you, the photographer, make all the decisions regarding this. This is done by setting different buttons or actually using an attached focusing ring that rotates on the camera lens. For those who like to have complete creative control of the finished product, this is the best focus mode.
In single auto focus mode, the camera automatically focuses when you press the shutter button either all the way down to shoot a photo or half way down to lock the focus. This mode is useful when shooting static objects.
In continuous auto focus the camera continuously focuses on the objects in the photo. In this mode the camera continuously corrects the focus as the objects distance from the camera changes. This mode is useful when you shoot photos of moving objects such as a race car during a race or airplanes during an air show. You can hold the shutter button half way down and continuously move the camera to follow the object. The camera will continuously keep the object in focus.
Like any other feature automatic and manual focus modes have their pros and cons. The first step to using them to your advantage is to understand how they work and what they were designed for. The next step is to experiment shoot photos using different focus modes and different types of objects and see how the camera behaves. Once you have done that you will be ready to instinctively use the best focus mode for each photo situation.