Definition : it's not quite the same thing as a directory because the sites aren't ranked but indexed. This means that for a given word the search engine will have a list of sites to suggest to you. To search for information you will give a list of keywords relating to the subject of interest and the search engine will in turn give you websites that relate as closely as possible to those words. For example: for a diet: dietary regime.
Registration : it's a bit more complicated than a directory. The search engine will simply ask you to fill out a field with your website's address and will then scan your website and pick out the important words. For that, we can give it a little helping hand (or a push in the right direction) by indicating what these words are in the html code of the site's pages. For more information take a look
here. Search engine examples: www.altavista.com, voila.fr, www.google.com. To make the referencing of your site with search engines automatic, some websites offer to do it for you. I would advise you against this. If you want something done properly, take the time and do it yourself.
Now let's take a look at how to optimize your referencing:
here