SEO is the other half of my professional life from web design, though really they go hand in hand. A simple definition of SEO is that it's the art of making a website rank well in search engines such as Google and Yahoo when someone searches on a phrase that the site is relevant for.
I'm what is known as an "Ethical" or "White Hat" optimiser. What this means is that I adhere to the guidelines set by the search engines and make no attempt to artificially inflate rankings by using dodgy techniques to fool the engines. My approach is to try to make the site I'm working on as good as it can be so that it deserves to rank well. If that isn't sufficient to get to the very top places then I look at how the site might be redesigned or enlarged.
I learned the basics of SEO while I was webmaster at James Thin, was taught a lot more while at Bigmouthmedia, but really became an expert at it when I joined Indicium Web Design and we took over Oyster Web and started handling more of the optimisation contracts rather than the web design ones.