SEO is Search Engine Optimization. In the context of the internet it involves the development of websites with the specific purpose of ranking high in a particular search engine or engines. Over the years the process has developed into a highly specialized field, which has become a profession in itself. SEO specialists with a track record are highly sought  after and command high 5 and 6 figure incomes.  The task of SEO involves the optimization of the web page code and content to maximize the probability of ranking highly, usually for specific search terms, or "Keywords and phrases".  Keywords and phrases can be as broad or narrow as you specify but generally the broader the term the more difficult it is to rank under that term.

Search engine optimization consists of many separate processes to enhance your sites visibility to the search engines. The biggest benefit of SEO is that the traffic you inevitably generate from your enhanced search engine listing is basically free. However the reality is that SEO takes a large amount of research work and generally a lot of trial and error before you realize any benefits from it. This research can take a lot of time and can cost a lot more than many other techniques. 

There are two types of SEO involved and both are necessary to do.

1. On-Site SEO

On-page optimization include optimizing individual pages for particular keywords so when search engine spider search for any given keyword then it can find those keywords on those pages.
On-page optimization include optimizing title tags, meta tags, alt tags, body content writing, Proper H1,h2,h3 etc tags use.

If on page optimization is done properly then and there is very useful contents on your website which are unique and not copied from anywhere else.
Search engine value unique content more then anything else so on-page optimization mean you have proper copy-contents for all of your pages.

2. Off-Site SEO

Off-Site SEO mainly involves "link building". Search engines such as Google gives more weight to website which got more links back from high ranking websites. The best web sites to link to are those that are classified as "authority" sites, such as Forums, Blogs and Article listing sites. Back links from these types of  websites add "authority" to your own website and enhance your listing under the relevant search terms for your website.

Search engines such as Google have now dominated the market to such an extent that statistics indicate that about 90% of traffic to most websites originates from search engines. Such has been the impact of Google, that it now exists as a verb in some dictionairies.

SEO is not to be confused with other terms such as "SEM" Seach Engine Marketing or PPC Marketing. SEO specifically involves what is termed "organic" search engine traffic.  That is traffic that is derived directly from unpaid search engine results.  SEM is a broader term that encompasses many other forms of online marketing such as "Article Marketing",  PPC or Pay Per Click Marketing.