for seo both are important on page and off page
on page relates to your webpage title, meta tags, meta description
off page relates to forums, blog commenting, directory submissions, etc.........

On-site SEO: The technique which is used to make on the page for the purpose of increasing ranking of that page in SERP is called "On-Site Optimization".

Off-site SEO: Off-site Optimization refers to a text and inbound linking from other website pages to your website pages.

Its a process to increasing the visitors of your website by doing different onpage and offpage seo techniques.

On page SEO means that you are making changes on the website.
Off Page SEO means you are making backlinks through different activities and you are generating the links from other sites.

Onpage optimization refers to all measures that can be taken directly within the website in order to improve its position in the search rankings. Examples of this include measures to optimize the content or improve the meta tags.

Off-page optimization refers to factors that have an effect on your Web site or Web page listing in natural search results. These factors are off-site in that they are not controlled by you or the coding on your page.