Crossfit is based, for the most part, on the findings of Dr. Izumi Tabata of Japan's National Institute of Fitness and Sports. The goal of his work was to see if he could improve the performance of athletes who were already conditioned to the elite or Olympic level of fitness.
He determined that a series of 8 (or more) 20 second intervals at absolute max output (95+% of max heart rate), each interval then followed by a 10 second interval of rest, improved VO2Max (oxygen uptake) by 14% and improved anaerobic capacity by a whopping 28%. The training period for this study was 6 weeks and each athlete warmed up (8 minutes or so) before beginning the protocol.
Keep in mind that this improvement was experienced by athletes who were already in peak condition.
What Crossfit did was take the Tabata Protocol (as it is called) and wrap it around the kinds of movements that active humans do in the everyday lives. The military, of course, adapts it to the movements and stresses common to soldiers.
As an additional note, I use the Tabata protocol in my workout on an irregular basis and can attest to its effectiveness. That said, it is grueling and often results in vomiting (the Crossfit mascot is "Barfy the Clown").
The Tabata regime is not recommended for folks who are not already extremely fit, but for athletes trying to ramp up for a competitive event, it is an excellent tool.