Search Engine Optimization is actually making your site visible to search engines, so that your site will rank well within the SERPs (Search Engine Ranking Pages)
Through out the nineties, and early 2000s, most search engine optimization was know as on page optimization because this meant modifying your page content/text so that search engines would like what they found on these pages, and index them.
A simple short summary of on page optimization
Title Tags: The most important of tags, this is is highly valuable for search engines to recognize what the topic/subject/theme of your page is. We are not talking about the title of your article in your page here, but about the HTML Title Tags that look like this:
If you go to your browser menu with your mouse, and click on Edit (Internet Explerer) or View (Firefox) you will find an option called "View Source", and that will allow you to read the HTML of the page you are currently looking at, and on the first lines of this page, you should see the title tag mentioned above.
Keywords: Keywords are as important as title tags, and these keywords should be used in your text as well as title tags, headings, and links.