Fighters don't usually fight at their natural weight. Most of them cut weight to be able to fight at a lower weight class. The weight they cut is not (usually) fat but water because it goes faster and you can get it all back in a day or two. They basically get dehydrated. Forrest Griffin is said to walk around at 240lbs but he fights at 205lbs so let's say he cuts 35lbs of water by saunaing (and/or other measures) and weighs in at 205lbs. Then the process of re-hydration begins, so what they basically do is start drinking again (not sure if IVs are legal but that would be another possibility). By the next day (fight day) he could theoretically be totally re-hydrated and in fact weigh more than 205lbs.
Fighters do it to gain a size advantage over other guys. Obviously nobody wants to give up that advantage so everybody does it (with few exceptions, most Japanese fighters don't cut much weight). There are extreme cases like Anthony Johnson who fights at 170 but looks as big as any 205er.
There are also negative side-effects. Obviously dehydration isn't a good thing for your body, especially for your kidneys. Losing so much water can be hard on your body and sitting in a sauna doesn't help much. In fact sitting in a sauna in counter indicated when you're already suffering from dehydration.