In On Page SEO, you can editing directly on the websites. You can add Title tag, Meta tags and other content optimization activity. And In Off Page SEO, you can not editing on the website but you can doing some link building activities for that.
On page optimization: This refers to all the things that you can do and throughout your website to ensure that the website home page ranks highly in Google, yahooor MSN. Off page optimization: This refers to what you can do to individual web pages or blog posts on your website or blog respectively to get those individual pages or posts to rank highly in the search engines like google, bing etc.
On page optimization is all about making your website search engine friendly Off page optimization is all about promoting your website to the search engines
On page work is to see that the site is properly functioning. Off page work is to enhance the quality of the site by getting good quality back links.