SEO turns your website more reachable and visible when someone tries to find it on the internet.
SEO is a set of tools and techniques to improve the position of your page in the search engines. When someone searches for a keyword related to your site in a search engine, SEO make your pages appear in the top results of the organic search.
The algorithms that decide the best results for a search keyword is a mistery hidden by the search engine companys. Over the time was possible to identify the best practices to improve the websites construction and structure. The keywords are also a important side of SEO, to diferent keywords, diferent results and positions are shown in the search engine.
SEO can be divided in two: internal and external factors. The internal factors are related to the website, clean URLs, use of web standards, page titles and a good structure of the pages (HTML Tags). The external factors are related to the links, or other pages, that lead to your website. The relations of your website with others, state a page rank by the search engines, a quality score based on the links and keywords that relate to your website. Google, for example, measure a website from 0 to 10 on their page rank.
It's important to distinguish the organic search results, and the paid search results. SEO deals only to the organic search.
The main objective of SEO is increase the number of visits on your site, reaching your clients and possible future ones, expanding at the same time your business. A good SEO work can increase your sales, reach more people, have more newsletter subscriptions or whatever your objectives are. SEO is a long term work, when your site reach the top positions in the major search engines, it will be by its own credibility.