SEO stands for Search Engine Optimisation. A person who conducts search engine optimisation enhances a website so that can reach a top ranking in Google or any of the other search engine results organic listings.
When you look at a search results page there are two types of listings on it. There is paid advertising, where essentially you bid a certain amount to have your listing placed there and each time someone clicks on that listing you will be charged a fee for that click.
Then there is the organic listings, this comprises the majority of the search results page and is the primary focus of an SEO Specialist.
Unlike paid advertising which is open to the highest bidder the positions in the organic listings are awarded to the websites that the search engines believe is the most appropriate website for that particular search phrase.