White hat SEO is the safest and most recommended (at least by us) way to go about your search engine optimization practices. These are the safest search engine approved ways of getting to the top of the rankings. Labeling your site properly, making it accessible, creating good webpage design and having a lot of content can be a great and organic boost to becoming an authority on a subject. In creating your content in natural and approved ways, you are ensuring that your site will stick around and not be banned for a long time.
Black hat SEO is the opposite. These are all the things you can do to try and fool the search engines. A black hatter takes what he knows about the search engine algorithms and tries to utilize various effects to work their site to the top. A black hatter could probably get an online shoe store to pass Nike and Reebok for the top spots...for maybe four hours. Some do it quite well but when they get caught, POOF goes the site never to be seen in the results on that engine again.
Gray hat SEO involves a mixture of the two. Someone in the gray will be using mostly white hat techniques while incorporating small amounts of black hat that the search engines might not penalize and usually don't ban for. For example, a site using a large amount of keywords on a page might make it read a little unnatural. This could be considered to have a high keyword density but not black hat keyword stuffing. This gray hat technique will probably get you higher in the ranks without the worry of a ban. But, you get a human viewer from Google on a bad day could result in a penalty for the site.
Some cloaking conditions may be a little more on the gray area, too. This is when you have a site dedicated to a lot of Flash or images and you are using keywords to describe what is in the flash so you can rank higher (without having too much text on your screen). Some cloaking is starting to be allowed for making mobile searching easier for phones and PDAs