Keeping things simple, an On Page SEO definition is that it is the creation of search engine optimized content using on page elements including text, graphics, tags and links.
It is impractical to expect that simply putting up a website with good content will result in it ranking well on the search engines and receiving lots of visitors. In fact the result is likely be that nothing happens. So if you want a high search engine ranking you need to consider on page SEO as you create your site.
Proper on page SEO is not an attempt to manipulate the search engines in any way it is simply the means by which you ensure that they understand what your pages (and posts) are about. In effect you are picking a keyword and telling the search engines that this page is highly relevant to that keyword.
Of course the search engines and their spiders do not really understand your page they are just looking for indicators of its relevancy. This will involve looking at the text in the title tags, in the header tags and in the image ALT tags plus looking at the links and their anchor text amongst other things. You can make your keywords more obvious by having some instances bold or in a larger font size. On page SEO can be viewed much like writing in a way that would enable a six year old can pick up on the subject without any need to understand the content as a whole.
If you convince the search engines that your content is highly relevant to your keyword you have achieved a vital first step but that will not in itself get a high ranking. On Page SEO can be thought of as what you say about your page, however, the search engines will not take your word for it and place more importance on what other people say about your page. Other sites can “vote” for your page by linking to it.
The important point to note is that if you do not say anything (your on page SEO is poor and the search engines are not sure what your page is about) it will be difficult to get a high ranking even with lots of backlinks.
Once you understand the on page SEO definition and the importance of getting it right you should analyse each page and make sure it is the best it can be.