A search engine is through which most of your potential visitors will discover your site. But for that to happen you first need the search engines in turn to discover your site.
It is only when the search engines 'understand' that your site is one of the best online places to find the kind of quality content that your site provides, is when they 'recommend' your site to people interested in similar content.
If all that sounds a bit abstract, allow me to elaborate.
Search Engines like Google, Yahoo and MSN routinely search the web for content and try to relate content to some keywords which they consider the focus of your content. So for example this tutorial on SEO is related to the term SEO. A web surfer looking for articles on SEO will query these search engines for the term 'SEO' and will get results based upon what search engines think are good sites for content related to the term 'SEO'.
In fact, a search on Google for SEO yields about 17,600,000 results at the time of the writing of this tutorial. Our web surfer looking for SEO related content would definitely not look beyond 15 or at most 20 initial links. The question then is how does the search engine decide which links to place before the other ones on such a search result.
Search Engines rank the pages for the specific search term and then show the pages in the order of those rankings. Google associates what is called a PageRank for each site. PageRank measures from 1 to 10, with a PageRank of 10 specifying a highly relevant site, and the relevancy decreasing in the order of the PageRank. Other search engines like Yahoo and MSN have similar ranking strategies. SERP (Search Engine Result Page) rankings in Google depend on the PageRank and also on how well the web site relates to your searched words. Given two web sites which relate equally well to your search term, the web site with a higher PageRank will be ranked higher in the SERP's.
Search Engine Optimization or SEO refers to how you can optimize your site such that your site is more aligned to the criteria that search engines use to rank web sites.
There is a lot of content online which will tell you a lot of stuff that you can do for SEO. Unfortunately most of these articles will tell you stuff that will waste a lot of your time and will not yield any desirable results. Worse, quite a few will tell you stuff that is outright wrong and are considered search engine spamming by major search engines. Using such techniques can result in your site being black-listed from their SERP's. Fortunately, there are still a lot of right things that you can do so that search engines rank your site favorably on your targeted search term.
The best part is, right here on this tutorial we tell you everything you should be doing and everything you shouldn't be doing for SEO.