Crossfit is:

Crossfit is: An intelligent combination of functional movement executed at high intensity.

The Crossfit objective: Increased work capacity across broad time and modal domains.
Functional movement can be defined as:

• Universal Motor Recruitment Patterns. This is ancient stuff. These are movements we have executed throughout history. Sitting, standing, throwing, punching, picking things up, pushing things overhead, pulling things, carrying things, running, jumping, swimming, and squatting repeated in multiple forms, fast and slow.
• It is natural. We will do the movements because they are divinely programmed into human DNA. Just like a bird flying or a fish swimming, we move around by using our legs, we lie down to sleep then get back up to work and play. Stronger people do these things with ease while enjoying better physical, mental, emotional health. Stronger people are more capable of facing whatever life throws at them.
• Core to extremity. The movement starts with the core anterior and posterior chain, moving outward to the extremities and radiating to the toes and fingers.
• Essential. We need these movements to live. We need to be able to sit, squat and kneel. We need to stand up. We need to be able to push our self up off the ground and carry things. We need to be able to repeat these things multiple times and with differing loads and speeds depending on what the universe calls for.
• Safe. The movements are natural and basic so, if done with intention and care are safer than single joint isolation movements which are unnatural and nearly useless on this earth. Isolation increases Injury.
• Efficient. We incorporate multi-joint movements to do the same work in less time as standard isolation work. More work in less time means higher efficiency. Translation: We get stronger quicker and safer. The smaller muscles grow in proportion to the required tasks.
• Effective. Crossfitters can carry large loads over long distances quickly. Not do a one time large load then need a full, big rest giving time for glances in the mirror. Not a long distance without load which is useful to get oneself to safety but leaves no ability to help another, pile sandbags, carry beams, lift a litter over uneven ground or hold something to assist another. Crossfitters can handle big weight over multiple distances with speed and then go do it again. This defines Crossfit. Real life stuff. Bicep curls, overhead isolated tricep extensions, cable flys, lateral raises are great for providing injury and silly for anything else, including ego. It took me sometime to understand this. My Pecs get hardly any attention now while my shoulders and elbows don't ache and my bench is 40lbs over my best Box Gym number at 52 years old. Crossfit is effective.

Intensity: There are five steps to intensity.
1. Submit to the fact that intensity is a slow steady on ramp to get to full throttle intensity. Take your time and enter the intensity lane smoothly. Too soon will get you hurt. Too slow you don’t make gains.
2. Do one rep correctly, starting with your body weight or a PVC pipe.
3. Do multiple reps correctly, increasing the load, slowly.
4. Time it.
5. Do it a few months later for a faster time.

The above is adapted from multiple sources.