Phase detection autofocus systems with multiple points have an array with lines of sensors that correspond to each AF point in the viewfinder. Which area(s) of the sensor are active depends on which AF point(s) is(are) selected. The shape of the PDAF array don't necessarily match the arrangement of the AF points in the viewfinder. In fact, they usually don't match. The light entering the PDAF array is divided by a splitter and aimed by microlenses to the appropriate areas of the PDAF sensor.
When a particular AF point is selected the camera pays attention to the corresponding pair of lines on the PDAF sensor. Exactly how this is accomplished depends on the overall design of the specific camera and its AF system as well as the particular settings for that camera selected by the user.
In general, the camera uses the AF point selected to measure how far and in which direction the lens is out of focus. It then tells the lens to move that far in that direction and takes the picture. The camera will use the highest area of contrast within the active AF area. Please note that the actual area of sensitivity for a particular AF point may be much larger than the square in the viewfinder representing that AF point. You'll need to practice and experiment with your particular camera to learn what the areas of sensitivity for each AF point are.
How accurately the lens moves to where the camera instructs is dependent upon the design of the lens, whether the lens has a position sensor that communicates to the camera exactly how far it actually moved, how accurate that position sensor is, and whether or not the camera is designed to take advantage of the information provided by the lens. For a more comprehensive answer that details this entire process, please see this answer to: If the focal plane is curved, should the outer AF points work correctly or front-focus?