Crossfit was first developed by former high-school gymnast Greg Glassman and his ex-wife Lauren in 1995. It has since exploded into a world wide fitness phenomenon. The workouts involve constantly varied lifts executed at high intensity.
The premise is that the workouts will prepare you for whatever life can throw at you and make you a better overall athlete. Crossfit athletes are proud of the fact that the can pull 400 pound deadlifts, run a 5km, or crank out dozens of pull ups at the drop of a hat (just make sure you have a good pair of exercise gloves).
Crossfit is definitely intense, but the workouts are scalable. As an example if someone can't do a pull up, resistance bands are totally acceptable. The workouts honestly aren't for people who have no gym experience whatsoever.
Those who thrive the most at Crossfit gyms (or boxes among the community) are people with a solid base in fitness already who want to push themselves to the next level.
The boxes can be as much as 5 times more expensive than your standard Gold's or Anytime Fitness. If you are inexperienced at some of the more complex lifts such as power cleans and overhead squats then it would definitely be a good idea to get some training before you switch to working out exclusively at home.
Working out at home is definitely an option, too. A power cage and a decent set of Olympic weights can get you an amazing physique from the comfort of your own home. Even if you don't have the space for a power cage you can still sculpt a six pack using the strictly body weight workouts.
As amazing as Crossfit is, there are a few things that I don't quite agree with. Personal records for different routines are a badge of honor in the Crossfit community. The desire to improve is definitely not a bad thing, but when the desire is so intense that it causes your form to suffer and the potential for injury to rise then there is definitely a problem.
Crossfit is an amazing fitness program that has produced stunning transformations. If you don't mind being a little uncomfortable and have the desire to catapult your fitness to the next level, then you should definitely give crossfit training a try.