It separates the focusing function from the shutter release button. At times, not all the time, but at certain times, it's best to allow the AF system to carefully determine the exact focusing distance, and THEN, to LEAVE IT SET at that distance, so that you the photographer, can devote attention to pressing the shutter release at a specific, "right" time. Much of the time this involves pre-focusing, because the action will occur at a specific spot, and your job is to WAIT for the action, then shoot it, or because it is slow, or difficult, or tricky to actually GET a good, accurate focus lock, due to whatever factor(s).
Back button focusing varies a bit with the level of camera. In the pro-level Nikons, there are actually TWO thumb button controls on the back; the combined AE-L and AF-L button, and the AF-ON. There are MULTIPLE combinations of how these three parameters can be set up to interact with one another. The "consumer" level cameras have a simpler set-up. Older Canons had no dedicated button, but instead used a Custom Function menu modification to turn the "*" (the so-called asterisk button) into an AF button. I beliece it was with the EOS 30D that the consumer Canon's got a dedicated AF-ON button, but perhaps that appeared with the EOS 40D?? Can't recall exactly. Anyway, under "some" scenarios, it's handiest to have the thumb button on the back set and then LOCK the focus once you let go; other times, you might want it to focus, with no lock, each time the button is pressed. This is critically important to remember--because it one does it wrongly, things can go south in a hurry.
The whole subject of BBF is too complex to go into here at much length. One concept though is the idea that the focus can be set by pressing a thumb button, then allowed to STAY at that distance, and then the camera's light meter can be allowed to "run free" as it were, without locking or "linking" both the metering area and the autofocus together using the normal shutter button half-press method that is the default. Of course, on some cameras, for some scenarios, it's advantageous to have the focus distance AND the light metering LOCKED TOGETHER, so that one can focus precisely AND take a meter reading and lock both of those parameters, and then re-compose and use the shutter release button ONLY to release the shutter and capture the shot--the focus AND the light metering having been done ahead of time, and neither parameter associated with the timing of the shutter's release.