Basically the on page is optimizing the page by insuring Title tags, Meta descriptions, H1 tags and Content are optimized for specific keywords. Off page is building links via methods such as article submissions, directories etc..
On page SEO is optimizing your web page itself. The name speaks it self. Off page is basically link building. Your page's popularity among other sites. I would recommend you to start with Google's SEO starter guide http://www.google.com/webmasters/docs/search-engine-optimization-starter-guide.pdf .