The following is from Albany Crossfit:

The portions in red are what I believe are the most important parts to understand from this post. It is what makes Crossfit work.

What are your thoughts on intensity? Is sweating more, grunting louder, going longer more intense? If you answered yes to any of those, clearly we are not doing our jobs of explaining CrossFit to you folks.
Intensity is very black and white. It is not arbitrary. We measure Intensity as Force x Distance/Time, and that's it.

Is moving more weight more intense? Think about it before answering. The answer is it can be but it also may not be. If you move a heavier weight through the same range of motion but it takes longer, it may actually be less intense.

Take a Deadlift for example, if Person A, deadlifts 200lbs and it take 5 seconds, and then deadlifts 300lbs but it takes them 15 seconds this is actually less intense. If a weight remains constant and is done faster, your intensity will go up. Take pull-ups for example if you do 10 strict pullups in 30 seconds versus 10 kipping in 10 seconds, kipping pull-ups are allowing you generate a much higher Intensity level.
Does this make sense?

CrossFit is all about intensity. Why? Because...Intensity is almost always the independent variable that maximizes the rate of return of favorable adaptation. What does this mean you ask? It means if you want to lose weight, burn fat, lower your cholesterol, decrease your resting heart rate, this is accomplished by increasing your intensity through workouts, as well as eating properly.
This is why it is so important to log your WODs. If your hit Cindy as prescribed and complete 11 rounds and then 2 months later hit Cindy again and complete 15 rounds, you have increased your intensity. How? Because you have done more work (4 more rounds of 5 Pull-ups, 10 Push-ups, and 15 Squats) then last time.

This is what separates us from the average "Globo" Gym. We care about and track performance. We are hitting WODs, that are measurable, observable, and repeatable. We are not just mindlessly moving a pin down a machine, or doing crunches, or half squats.
Please, ask questions, post to comments. This is important stuff and we really want you all to understand this. Feel free to talk to us about this during class too.