On page search optimization is optimizing the actual content of a website that is seen by the user (or more precisely put, optimizing the content on the page, not all of which a viewer may see).
This allows you to independently control what searches are more likely to have potential customers directed to which pages within a website, allowing more precise targeted advertising and similar personalization methods to be performed; instead of greeting each visitor to your website with the same front page, based on what search they found your page in you can send them to a page of the site specially picked for them. More importantly, on page optimization can be used on text on a webpage to help increase its value with search engines heavily, making your website a much higher hit on the lists of thousands of hits Google comes up with whenever anything at all related is searched for. It is one of the biggest components of optimizing a website for search engine use, but is vital because it is the fundamental factor that determines how much traffic SEO will be able to acquire you at the very most, and essentially gives you free advertising by expanding the audience that sees your site.