Black Hat SEO is, in its simplest definition, using trickery to gain success with a web site with the search engines.
A number of tactics have been used over the years to trick or deceive the search engines. Some of the most popular include hidden text, where words are placed on a web site in the same color as the background. They are in effect, invisible to visitors to the site, but can be spidered by the search engines.
Keyword stuffing is another popular tactic where in as many keywords can be placed on a web page as possible. Even if the search engines ignored this tactic, most likely your visitors wouldn't. They'd catch on to the fact that every fifth word is the same or that the sentences seem awkward. Their focus becomes the words on a page, not their meaning.
Cloaking is like a shell game. You seem to show one page to a search engine, then redirect them to another, often a page filled with keywords.
Link farms are about putting up a site whose sole purpose is to list links. The only reason to have a link farm is gather links and serve no other purpose.
As a SEO Consultant I use only ethical methods to help my clients. My objective is to inrcrease traffic to a site, but not to put a site at risk. Black Hat SEO could result in not just a drop in rankings, but a drop from the search engines completely.