The basic formula for CrossFit is: Functional movements, performed at high intensity, with constant variance.

Functional Movements: Since the 70s we have truly screwed up weight lifting. Specifically referring to the development of workout machines. Machines isolate one muscle generally on one side of the body, and therefore cause major muscular balance issues. CrossFit is taking exercise back to a more primal focus of multiple joint exercises that condition the body for actual functions that it will be required to perform. There are two things that bicep curls and tricep extensions make you better at... bicep curls and tricep extensions. They do not help lifting heavy boxes or pulling heavy loads, etc. What are you bettering yourself at?

High Intensity: Short intense bouts of exercise are extremely efficient. It's all about power. P = (f*d)/t. In this equation time  (t) is the greatest influence of power. If the time is reduced slightly power will increase greatly. Instead of spending hours at the gym, scientifically data proves that better results occur in shorter amounts of time i.e. 15 - 30 min of intense activity.

Constant Variance: Muscles can adapt and condition themselves for certain exercises and energy systems. Example - try telling an Olympic lifter to run a 5k much less a marathon. To avoid this specialization from occurring consistent variance is important to keep the brain guessing and condition the body for anything and everything else it might face.  With variance we increase our bodies general physical preparedness.