This is a pretty simple explanation and many people have different answers to this but the gist of the answer to this question goes like this.

Black Hat SEO's optimise websites in non-traditional ways using techniques that are frowned upon by the search engines and can go against their terms of service. There are many grey areas when it comes to what you can and can't do, black hat SEO's operate in this grey area a lot, pushing the boundaries to get rankings.

White Hat SEO's use techniques that are widely accepted as common practice and won't do anything to jeopardise a website or project. OK, so which one's better? There's no easy answer to this. It really depends on your attitude to risk and the results you're trying to achieve. If you have a business website that brings in allot of customers for you than a Black Hat SEO might not be the answer for you. Then again, it depends how much you're willing to push the boundaries with your website.