Meta tags or Meta Data: This is the information about a web page in the header of HTML code. Meta information is sometimes referred to as "information about information." Meta information tells search engines what information is contained in the page. This meta information helps search engine spiders, often called "bots," understand your web page. Bots are the "elves"of the Internet that scour all pages on the Internet and create an index. It is important that your pages are properly coded to provide bots with the information they are looking for, presented in a format they can understand. Also, when prospects use search engines to find your site, they are shown the title and meta description. It's from this information that prospects decide whether to click on the link to your site. While meta tags aren't as important as they were at the advent of browser-based computing, it's still very important that meta information be unique, correctly presented, and complementary to your title tags, page content, and links.
On Page Optimization: This term refers to working within your website itself to improve relevance with Search Engine Spiders. This includes taking steps to make sure that the information on your page exists in such a way that it is easily digestible by bots.
Off Page Optimization: This is a fancy way of referring to the practice of getting text links that point to your site from another trusted source. For example, if you are Financial Advisor in Charlotte, NC and Charles Schwab has a link from their home page that says, "Charlotte Financial Planner" - that is a very good thing for two reasons. First, Charles Schwab is an authority in the area of personal finance, and search engines value links from authority sites. Second the link itself has text that tells the bots that Charles Schwab is linking to the Charlotte financial advisor for a topic that is relevant to both of their sites. This type of link is complimentary and makes the most of the power of the link hand-off. There is much more that can be done with Off Page Optimization, and there are nuances as to how the links should look and whether you should consider providing a link back to the party that links to you.