On-Page SEO refers to the SEO techniques that improve the quality of a web page.The On-Page SEO methods typically involve editing the page content, bettering the code and perfecting the URLs and navigation to make it search engine friendly.

Onpage SEO is a process to make every page of website search engine friendly. It includes following activity:
- Page Title Creation
- Meta Tag Creation
- Alt tag creation and optimization
- Content optimization
- Making URLs SEO friendly
- Resolving canonical issues etc

Onpage consultancy around the site design (like a site map, page linking, link tagging etc), page tile, page description, page contents, unique key word or most common with site product etc.

Generally we consider all those techniques in ON page which helps to make our website more SE friendly.It can be a website design,meta tags,robot.txt file,content,keyword research etc.For more detail you can read tutorials about ON page.
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You must consider two things when you speak of on page and those are meta tags and content.

On page optimization is one of the very first steps of SEO. If you can do proper on-page optimization for your website you can not only rank well in a search engine but also can increase the overall readability of your website for your visitors. On Page is all about content, content must be unique and useful to get attention of search engine as well as users. Above One member of forum have define the on-page activities very well in his post....

"On Page" SEO simply refers to the text and content on your web site pages. Basically editing your page and content so the Search Engine can find your webpage when a surfer is searching for your web sites particular topic.

It is an optimization technique that is directly done on the web pages to achieve a good page rank over search engine.

Nowadays you should pay much attention to onpage seo as content and canonical issues