On Page SEO, short version, involves all the words that you can see on your web site's pages. How this content is optimized for the search engines is just one component of effective SEO. Here is where key words and key phrases get put to good use. Captions, headlines, paragraphs, footers, disclaimers, etc. are all a part of On Page SEO.
Off Page SEO, succinctly, is everything else. Some of the off page factors include: linkage on the site, both internal links and external linkage; writing the text of internal links themselves; building site popularity through tweeting, commenting on forums and blogs, press releases, submitting to directories, etc.
There's a lot that goes into search engine optimization - and there's lots of stuff out there on the web for you to read about SEO, if you're interested. (Read Google's SEO overview here.) There's also lots of people out there claiming to know all about SEO. Maybe they do, maybe they don't. Ask for examples of their accomplishments before you pay them anything.
Meanwhile, consider this. The purpose behind optimizing content is to get your content noticed and highly ranked in search results on its themes or topics by the search engines. Which for most folk mainly means Google. You're competing with other content to get into the top spots.
Google is in the business of competing with other search engines to provide the more informative and on-target results to its reader's search requests. If Yahoo could give you better results (and you should compare them often -- Yahoo gives better locator information IMHO, for example) then you'll switch to Yahoo, right?
It's really not rocket science. Write the best content possible for your topic. Think of your reader, and help them here. Give them your expertise. Give them links. Give them information in easy to follow language.
Help Google beat its competition, in other words. Do this, and do this well, and you've achieve your SEO goals automatically.