I'll give it a shot - it's not easy to explain though, I bracket raced for about 2 years before I understood it fully. Basically you tell them how fast you are going to run and you are racing against yourself - if you go faster than that then you lose (unless the other guy goes faster than his time by more than you). First of all, a PERFECT reaction time is . 500 seconds (most of the time, some trees are . 400 trees - usually that's called a pro tree). Secondly understand that your times do not start until you leave the line - in other words you could get the green light and sit there at the line for 30 seconds and still run a 10 second 1/4 mile.
Let's look at scenario #1 - racer A dials in at 20 seconds, racer B dials in at 10 seconds. They both stage, racer A's tree comes down and he gets the green light and takes off and cuts a PERFECT . 500 R/T. Exactly 10 seconds (the difference between their dial ins) later racer B gets his green light and he also cuts a PERFECT . 500 R/T. If racer A ran a perfect 20 second run and racer B ran a perfer 10 second run they would arrive at the timing lights at the exact same time and it would be a tie (has this EVER happened in history? I doubt it).
Scenario #2 - same dial ins and reaction times (. 500), but racer A runs a 20. 5 1/4 mile and racer B still runs a PERFECT 10 second run. Now racer B got to the lights . 5 seconds before racer B and wins. Racer B in this case could have run anywhere from a 10 second to a 10. 499 second run and still won.
Scenario #3 - same dial ins but this time racer A has a reaction time of 1 second and racer B still runs a perfect . 500 R/T. Racer A runs a PERFECT 20 second 1/4 mile and racer B runs a PERFECT 10 second 1/4 mile. Racer B will cross the finish line . 5 seconds ahead of racer A and win. This is because his combined reaction time and 1/4 mile time is perfect (10. 5 seconds) and racer A's is . 5 seconds slow (21 seconds). In this case once racer A left the line it was impossible for him to win because racer B cut a perfect light and time.
Scenario #4 - same dial ins and reaction times as #3 (A=1 second, B=. 500). Racer A runs a 19. 5 second 1/4 mile and racer B runs a PERFECT 10 second 1/4 mile. They will cross the finish line at the EXACT same time but racer A loses because he was . 5 seconds FASTER than his dial in time!
Scenario #5 - same dial ins but both have a perfect reaction time of . 500. Racer A runs a 19 second 1/4 mile, Racer B runs a 9. 5 second 1/4 mile. In this case Racer B wins because he broke out by less than racer A.
Confused yet? Now you know why it takes a long time to figure out bracket racing! Basically your goal is to have a perfect reaction time (or at the least a better reaction time than your competitor) - and IF you have a perfect reaction time then you want to cross the finish line just in front of your competitor. If you do that you will win as long as you both don't run faster than your dial ins. Bracket racers that know their stuff watch the guy in the other lane and if they are too far ahead of them hit the brakes so they cross the line just in front of them (thereby being assured of not breaking out - assuming the proper reaction times, yada, yada). Bracket racing is truly a thinking man's game!!
-Steve
EDIT - just saw BCFASTS reply - took me about 30 minutes to draft mine, his was a lot more concise but didn't get into the details that take time to learn. Did you bracket racers see anything wrong in my description - I could've screwed something up?