This is a website that has been optimised so that it is easy for search engines to read and understand its pages and its structure so that it can be accurately indexed in search results.
The robots and spiders that crawl the web are automated so they cannot make judgement calls as humans do. Mathematically they have to ask "Is the site I'm looking at more about subject X than the other site I went to earlier?" If the answer is "Yes" it will rank higher.
The aim of search engines is to be as human as possible but their greatest fault is not being able to understand graphics - a major part of what makes modern websites user friendly.
The skill of an SEO company is to maintain the user experience through graphics while making sure the robots and spiders understand each page, the whole site and the structure of the whole site.
Ultimately they're job is to try and persuade the robots and spiders that "this page is the most relevant for keyword X or phrase Y". This is partly through the code underneath the site and (sometimes) partly through increasing the profile of the website elsewhere on the internet.
I'm Tim Hill, a Search Engine Optimisation and Online Marketing specialist. I created this site to help others understand that SEO is not a mysterious black art!.
If your a newbie try the Getting Started in SEO page, otherwise feel free to dig around and learn more.