Originally, SEO was a method whereby "tech head" marketers would influence the SERPS (search engine results page) by reverse engineering the top pages in the SERPS for a given keyword. The top influencing factors would be measured and averaged out to establish a baseline for ranking for a particular word or phrase.
It was remarkably easy for those in the know. And it was very ripe for extreme manipulation. Therefore as time moved forward search engines like Infoseek, Go, and Alta Vista started looking at alternative means of ranking their index of pages. Exotic engines like Direct hit would measure how long you stayed on the page you clicked and how long before you came back if at all. (Interestingly, Google is employing similar technology today. It is why they are trying desperately to get us to be signed in as we use Google.)
As it became easier and easier to manipulate the engines. It was obvious that new methods needed to be employed in order to rank a page.
And along came companies called Inktomi and Google. The former looked at the number of links coming to a page. Commonly called link popularity. The latter uses the value of the link, which comes from the value of the page, which comes from the links to that page. And so on and so on, ad infinitum.
Today, we see Google needing to measure the ever exploding social web so that it can measure... drum roll please. The value of the social pages growing at a geometric level on the social web.
The Short Version Please
OK here is my Cliffs Note version of SEO. SEO is the act of targeting a keyword phrase on a page, and then optimizing that page for that phrase. Then hopefully, the content on that page will generate enough interest to get links from other pages on the web such that your page will gain favor enough by the engine to rise to the top of the SERP.
By paying attention to SEO you can get your brand reputation and your services found. And therefore create more leads and more sales.
Google, Bing and Yahoo pay attention to all the social networks as best they can. They also are doing their best to create their own social networks.