Black hat SEO refers to employing tactics which are frowned upon by and can get you in big trouble with Google and other search engines. These are tactics which are seen as just being used to game the search engines and achieve better rankings for the websites/pages which use these tactics, whether or not those rankings are truly deserved based on their own merit of good content.
Examples of Black Hat SEO
Keyword Stuffing – This is one of the oldest black hat methods in the book. It's also very easy to pick up on. Search engines used to be much simpler and relied almost exclusively on keywords on a page to filter their search return results. Therefore, early SEOers would simply repeat the keyword or keyword phrase over and over on a page, sometimes using tricks like disguising that text as the same color as the background to make it look natural to visitors.
Hidden Links – Similar to what I just mentioned but it involves hiding content on a page from visitors while search engines can still see it.
Cloaking – This refers to serving up two different pages of content for seemingly the same page – one optimized for search engines and something completely different for your visitors.
Doorway Pages – Using multiple pages as entrances to your site which are all optimized for different keywords.
Paid Links – Buying dofollow links is a major offense when it comes to link building. You're still allowed to purchase banner links and other advertisements so long as the links don't pass any link juice.
Link Blasting – This refers to typically using automated software to create links en masse to your website. This used to work but it's a terrible idea nowadays and very easy to detect, at that.
Blog Networks – Another link building method where you are basically purchasing links from an established authoritative network of blogs with a lot of link juice to pass around.
Anything Unnatural – Really anything which can be considered unnatural with regards to SEO is considered black hat, so if you're ever in doubt over something you are doing to improve your rankings, odds are Google won't like it. Stick to my white hat SEO examples instead, methods which are evergreen to SEO.