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CrossFit is a nutrition and exercise regimen that incorporates elements from all corners of the fitness world, aiming to create a broad, general, and inclusive fitness. We do this through various combinations of weightlifting, gymnastics, and cardiovascular exercises. A great, detailed introduction to CrossFit can be found in their "What is Fitness?" article, written by Greg Glassman, the founder of CrossFit.
Traditional HIIT training is often done with very little regard to form or technique, whereas CrossFit has created standards of every movement prescribed in the workout. Performance is recorded, and you can visually see progress by faster completion times, lifting heavier loads, or completing more reps within a given time. This style of fitness is observable, measureable, and repeatable, features that are not often found in the HIIT space.
CrossFit is designed to be infinitely scalable. You should always use a weight that's manageable for you, rather than attempt the weight prescribed, and substitute movements you can do. Coaches can help here, but for general recommended scaling, follow @CrossFit Training on Instagram. The CrossFit Journal also contains resources to help you scale the workout to your level.
The best way to understand CrossFit is to experience it, so stop in the gym and come work out!
If you'd like to do more research on CrossFit and its methods, these resources are incredibly valuable.