SEO stands for Search Engine Optimisation.
If you search Google for information and it gave irrelevant search results (you searched for apples and it showed you websites for tractors) you would stop using it pretty quickly, which in turn means the advertisers (like the results down the right of the page) would stop advertising with them and they go out of business!
So what they do is send computer programs into your site (called spiders) that record/catalog/index the contents of your site, this happens at indeterminate intervals and times not when a site is searched for as it needs to index it before it can give it in search results.
Now these programs are clever and know that typically a subject matter would probably have certain relative words that appear in such an article, it also knows that typically these words would be repeated a certain amount of times.
There's a lot of other criteria that the “spiders” will use in order to say “heh, this page would be really good if someone searched for ______”
Still with me? Hopefully your saying well that makes sense and is kind off obvious…good.
So search engine optimisation is what it says. Its optimising your site to make it as friendly as possible for those search engine “spiders” to “crawl” your website and now exactly what the area of expertise is by the writer of the text.
SEO is defined by Wikipedia as 'the process of improving the visibility of a website or a web page in search engines via the “natural” or un-paid search results’.