AI Servo is the name of Canon's continuous-servo autofocus system, that continuously tracks a subject. As long as you are half-pressing or fully pressing the shutter release, (or using the popular AF-ON technique) the camera's autofocus system will continuously track whatever subject is under your selected focus point.
This autofocus mode is useful for tracking moving subjects, and is also useful for focusing at very shallow depth (fast apertures) when shooting hand-held in very close-up situations. (Focusing on a bride's eyelashes using an f/1.4 aperture lens, for example)
Technical explanation of AI-Servo Autofocus
Most professional cameras, Canon or other, have two or three main autofocus "drive" modes. Single focus, continuous focus, and sometimes a hybrid or automatic AF mode that decides for itself which of the other two modes to use. (Most serious photographers will want to ignore the third focus mode and take control of how their camera autofocuses, unless they find themselves in a very specific situation that actually benefits from the camera making the decision for them.)
AI-Servo is the name of Canon's version of continuous-servo focusing, and "One Shot" is the name of Canon's version of single-servo focus mode.
In single focus mode, when you press or half-press the shutter the camera will focus on the subject once, lock that focus, and stay there until you click the picture or until you take your finger off the button.
In continuous, AI-Servo autofocus, whenever you press or half-press the shutter, the autofocus will continually change focus in order to keep the subject sharp, even if the subject or the photographer are moving.
This is especially helpful not only when shooting action photos of moving subjects, but also when shooting at super-shallow apertures such as f/1.4, and especially at close distances of just a few feet, because in these conditions even the slightest movement can throw the desired subject out of focus. Of course in such difficult conditions, both One-Shot and AI-Servo can fail to deliver 100% keepers, so shooting multiple images is highly recommended no matter which focus mode you find works better for you. Some of the latest Canon cameras, when focusing in AI-Servo, can also automatically move the focus point around the viewfinder to track a subject that is not just moving towards the camera or away from it, but laterally through the viewfinder.
A Note About Focus Point Selection:
These two main focus modes, AI-Servo and One Shot, are mostly separate from the other focus point area or focus point group option. Those allow you to use a single focus point, a cluster of 5-9+ focus points, or all the focus points at once. In other words, most of these focus point selection / area modes can be selected while in either single or continuous AF.
However there are indeed some focus point selection modes that are only available during continuous autofocus, such as 3-D focus point tracking which automatically moves the focus point around the viewfinder to track the subject you first lock focus on.