I probably quallify as a ->

, but here goes...
DSLRs all

use passive autofocus (they use the available light to decide what's happening). Autofocus assist is where extra light (flash/IR) is beamed out to illuminate the scene.
How the A-focusing works is that as the lens searches from one end stop to the other all of the N points are simultaneously evaluated (assuming all are selected).
Each AF point is divided into a number of segments vertical and horizontal (not sure how many in each segment >5 probably). As the lens travels from close->infinity the contrast between adjacent segments is evaluated. When this reaches a maximum (above a certain theshold depending on the level of ambient light) then the scene is deemed to be in focus.
A nice edge is best, as you've probably noticed. This is because a sharp difference in contrast can be detected.
If you assume 5 segments in a horizontal axis then what the AF point on the camera "sees" the lens tracks is something like this:
55555
44566
33477
22288 <- Sharpest difference in contrast = focused
33566
55555
This also explains why in low light conditions the camera "hunts". Also why you can't focus (easily) on a sheet of paper, but it is a doddle to focus on its edge. Low contrast situations are hard for the AF to work on.
Finally... it is possible to have more than 1 point active at the same time if more than one area "triggers" sets the I'm in focus now flag. In which case the camera is "happy" since as far as it cares the scene is focused "click"
Of course it's not quite that simple, but the clever CPU's hanging off the back of the AF point do all sorts of algorithmic munging to work this out
Hope that helps