On-site SEO refers to all the things you do on your own website to optimize it for search engine discovery. On-site SEO includes things like writing page title tags, meta description tags, and updating H1 tags. It also includes things like creating interesting on-site content (daily blogging, or landing page content) that contains your specific keywords. Finally, it includes all the technical aspects of SEO, such as making sure that you have a clean sitemap, making sure you have the proper 301 re-directs in place, and anything else that is behind the scenes on your website, but that helps you get noticed by search engines.
Some people think of on-site SEO as a more foundational side of search engine optimization. Once your on-site SEO is taken care of, you need to focus on off-site SEO, which is the side of SEO that helps you rise significantly in the rankings.