There are 2 types of search engines: Search Engine Spiders and Search Engine Directories. Each search engine uses unique criteria for "ranking" sites - this "ranking" determines their placement in the search engine results page (SERP). Spider-driven engines use robots to spider sites on the Internet. Robots "crawl" each site and "score" pages based on relevancy. Directories have humans that check the sites - rather than robots. Some engines score the index page while others score individual web pages. The goal of search engine optimization (SEO) is to get higher rankings.
In the web's early days, it used to be that a search engine either presented crawler-based results or human-powered listings. Today, it extremely common for both types of results to be presented. Usually, a hybrid search engine will favor one type of listings over another. For example, MSN Search is more likely to present human-powered listings from LookSmart. However, it does also present crawler-based results (as provided by Inktomi), especially for more obscure queries.
SEO is short for "search engine optimization." To have your site optimized for the search engines means to attempt to have your site appear in the top of the search engine results pages whenever a specific keyword is typed into the query box. Search engines have two types of listings: those that are paid for, which are usually distinguished as "sponsored links" and those that are organic.