From Wikipedia:

CrossFit is a strength and conditioning brand. CrossFit combines weightlifting, sprinting, and gymnastics. CrossFit says that proficiency is required in each of ten fitness domains: cardiovascular/respiratory endurance, stamina, strength, flexibility, power, speed, agility, balance, coordination, and accuracy. It defines fitness as increased work capacity across all these domains and says its program achieves this by provoking neurologic and hormonal adaptations across all metabolic pathways.

...Classes at affiliated gyms typically include a warm-up, a skill development segment, and a high-intensity workout that lasts around ten to twenty minutes. Affiliates create a new workout each day called the "Workout of the Day" or "WOD". Affiliates often use scoring and ranking systems to transform workouts into sport. Some affiliates offer additional classes which are not centered around a WOD, such as Olympic weightlifting classes. Some CrossFit athletes use the free workouts and instructional videos available at the CrossFit, Inc. website, in lieu of attending an affiliate.

The idea behind Crossfit is to push oneself through high-intensity training circuits in order to build functional athleticism which can theoretically be applied to other disciplines.

If you meant 'what has crossfit got to do with paleo?'... paleolithic man was 'physical' in a very specific way... short bursts of activity, interspersed with very heavy, intense, lifting/carrying/heaving (eg hauling a dead animal back to the cave)... crossfit, some would say, mimics paleo 'exercise'

http://www.youtube.com/watch?v=WjdQZxTIj1U

From the ultimate source: http://www.crossfit.com/cf-info/what-crossfit.html

"Constantly varied, functional movements executed at high intensity."

Crossfit is awesomeness.

It is also kind of cultish, just like paleo :) They really get you hooked! I've been doing it for 3 years, and just can't quit it!

On a serious note, the wikipedia quote is spot on. One thing it doesn't mention is the community aspect. You will get a strong sense of community and support in most CrossFit affiliate gyms. Not all though, so if you want to try it, do your research first.

Constantly varied, functional movements done at high intensity. It revolves around movements that are natural to the body rather than isolating "parts." It is paired with Paleo because Paleo is thought of a a "natural" way of eating..CF is a "natural" way of exercize.

I love what Robb Wolf said about it on Nightline...it's like a tribe. Other than the workouts themselves, this has been the biggest difference I've seen at my gym. I know everyone there and we have a common goal. I truly miss my gym when I'm gone!

The igx couch thread has, eventually, buried within it, an interesting view of Crossfit. Not linking, you can find it on your own.