Raw food diet is basically just a mixture of uncooked meat, plus other additives which make up a complete meal and mimics what a cat would eat in the wild. In the wild a cat would eat a whole animal, which includes muscle meat, but also organs and bones etc.
People favor it for a number of reasons, like feeling that it is "as nature intended", and having a much higher caliber of meat and no "fillers" (ingredients like grains which add calories but are thought to not have any nutritional benefit to cats) like most of the commercial foods have. And if you are brave enough to make your own, then you have a much higher degree of quality control than any other food you can buy.
There are a lot of ways you can feed your cat raw food. Many people make their own (there used to be a lot of VERY vocal proponents of this, so if you do some searching in the forum, can you find these posts). They get a meat grinder, find a local source of the raw meat(s) that they are going to put into it, learn what other additives they need to add, and then make big batches of food and freeze them. There are books, facebook groups, websites etc., that are dedicated to people sharing this kind of info.
If becoming a mini "cat food manufacturer" isn't for you, lots of pet stores now sell raw food. There are quite a few brands of frozen raw food you can buy (the one I use is here:
http://www.radfood.com, but there are many others too). Also, the "high end" pet food stores tend to also sell freeze-dried raw food. I've never tried those, so couldn't tell you much about them. There's a pet food store near where I live which will also sell you just the meat (frozen) and then sell you all the additives too (bone meal, taurine etc) which would make it complete. So there are lots of options available.
The downside of raw food, especially if you "roll your own" is that you are feeding something that may not be nutritionally complete, which could case various health problems for your cat. So feeding raw is not something you do "half way". Bringing home a pack of ground beef from the supermarket and tossing it in your cat's dish and calling it a "raw diet" is not something you want to do!