Single-Servo focus is any autofocus system that focuses on a subject once, and then stops focusing. The acquisition of a focus lock is often indicated by a beeping sound from the camera. The photographer is able to then fully press the shutter release and capture images, and/or re-compose their framing. The autofocus system will stay locked until the photographer removes their finger from the shutter release and presses it again.
This autofocus mode is useful for photographing any static scene, or a subject that is not moving.
Single-Servo Focus Mode Explained
Most professional cameras have two or three main autofocus "drive" modes. Single-servo focus, continuous-servo focus, and sometimes a hybrid or automatic AF mode that decides for itself which of the previous 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.)
In single-servo 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. This focus mode is useful for any static scenes were motion is not a major factor, and/or where depth of field is not critically shallow.
In other words, a photographer may choose to use single-servo autofocus for action, if they are shooting with great depth of field such as f/8 on a wide-angle lens, and oppositely, they may choose to use continuous-servo autofocus for a still, motionless subject if they are shooting with extremely shallow depth of field, such as f/1.4 on a telephoto portrait lens.
In continuous-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.
A Note About Focus Point Selection:
These two main focus modes, continuous and single, are mostly separate from the other focus point selection settings, area, or AF point group options. Those separate options 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 dynamic 3-D focus point tracking (Nikon cameras) which automatically moves the focus point around the viewfinder to track the subject you first lock focus on.