Black hat SEO refers to optimization techniques that you can use that are against search engine rules, for example buying keyword rich backlinks to up your rankings. Often these techniques can increase your ranking without a huge amount of effort in comparison to white hat technqies (strictly within search engine rules, and more time consuming and lengthy) but can ultimately (and rightly so) lead to a website being removed or penalized in the SERPs when the use of such techniques is found - a well publisized example of this is the JC Penney case at the start of this year. Not too sure what gray hat SEO is to be honest, but I'd take a shot at saying it's the gray area inbetween bacl and white hat SEO, and the techniques that fall into that category would vary based on people's opinions I think...

White Hat SEO refers to the usage of SEO strategies, techniques and tactics that focus on a human audience opposed to search engines and completely follows search engine rules and policies Or any SEO tactic that maintains the integrity of your website and the SERPs (search engine results pages) is considered a "white-hat" search engine optimization tactic.

Blackhat SEO*is a select set of techniques that should not be used for search engine optimization of any website. Most of these techniques are devised to get a better page rank, by using unethical methods disapproved by most search engines.

Often in the world of SEO, the difference between what is allowed and what breaks the rules is intent. The ‘grey hat’ idea came out of this – a list of techniques that can be used for good or bad purposes.

Some of the common grey hat techniques are:

1.Paid Links. Paying someone for placing a link to your site on their site or vice versa is a questionable technique.
2.Duplicate Content. Recently, duplicate content on the web has become an increasingly significant problem for both search engines and search engine users.
3.Micro Sites. While this can be a great "white hat" technique when used right, micro sites are being abused by some SEOs.
4.Link buying – Google strictly prohibits link schemes, but sometimes money can change hands for links without it being a scheme.

Black head seo means you are using the techniques that are against the search engine rules, white head refers using SE friendly techniques, in terms of content, keywords tags, alt tag and it also includes off page activities.

great and nice post you have post

White Hat = No Search engine's rules violation
Black Hat = Search engine's rules violation
Gray Hat = White Hat + Black Hat

Black Hat SEO is ignoring the checklist and using banned methods which will eventually hurt the website when they get caught.
Grey Hat SEO has two possible meanings:
1. A mix of white and black SEO.
2. Using SEO which is not white or black, but in a middle area which is sneaky, but not banned because its still legitimate.
White hat mean your doing legal work and its took like natural traffic on your site.