Canon EOS 5D Mark III Instruction Manual (en)

Depending on the scene, position the subject toward the left or right to 
create a balanced background and good perspective.
In the <
A> mode, while you press the shutter button halfway to focus 
a still subject, the focus will be locked. You can then recompose the 
shot and press the shutter button completely to take the picture. This is 
called “focus lock”.
In the <
A> mode, if the subject moves (distance to camera changes) 
while or after you focus, AI Servo AF will take effect to focus the subject 
continuously. As long as the Area AF frame covers the subject while 
you press the shutter button halfway, the focusing will be continuous. 
When you want to take the picture, press the shutter button completely.
A Full Auto Techniques (Scene Intelligent Auto)
Recomposing the Shot
Shooting a Moving Subject