K-1 World Grand Prix is a fighting venue similar to those of cage fighting, like
UFC. However, this sport places fighters in a boxing ring and lets them wail on each other with gloves. It's more like boxing on steroids than anything else, with a variety of martial arts thrown in the mix.
Each fighter has their own style, whether it is Karate or Kickboxing (the 'K' in K-1 stands for karate, by the way). In the ring you'll face opponents of all styles, and you'll have to learn how to cope with each if you're going to succeed.
There are various generic game types to choose from, whether it's a simple Exhibition match, or the World Grand Prix Championship itself. Advancing through the Championship circuit will unlock various things like training modes (not really worth the effort), or a chance to take fighters' robot counterparts into the ring. This mode looks nice and is fun for a while, but it ends up being the same fight with Virtua Fighter 1-style characters.
What K-1 really lacks, though, is the ability to create your own fighter. There is some degree of customization during the Championship, where you get to train your fighter and increase or decrease their stats. You can then use them in Exhibition matches, but that's the extent of it. Mucho points would have been awarded if you could make a character from scratch, a feature that will hopefully be included in the sequel (if there ever is one).