What is this and what does it do? In regards to websites.

I am not sure what you are referring to by META, if you are speaking of META Tags they are the set of information that is at the top of your code. It allows you to tell people in the top bar of their browser what your website title is and what they are looking at, it also lets search engines know what your key words are for your website along with a decription. This is the VERY BASIC answer to your question.

META tags are meta data about your web page, that is, they DESCRIBE your data. People don't see them, rather they are used by web browsers and web crawlers (i.e. googlebot, which roams around the web archiving and indexing web pages).

A common use is (but much less so now) used to define keywords relating to your site. Googlebot (and other web indexing services) would get to your page, see the META keywords, and say "Ok, Prodigy's website should show up when a user types in the following keywords into the search engine: 'Real Estate', 'Sell Homes', 'Prodigy's Website')
The problem with this method is that it is completely up to the webmaster to be honest, that the keywords he is entering actually relate to the site. Unfortunately, this didn't happen, people would enter EVERY keyword they could think of, even if it had nothing at all to do with his site. I believe web crawlers now mostly ignore these tags, though there are others they still follow. This is definately a quick research project you should work on.