Google's brand name for its keyword sensitive paid advertising. Google Adwords sells placement on the Google website and partner websites through a bidding process. Advertisers on Adwords range from the very small advertiser with a $20 monthly budget to the very large with multi-million dollar budgets. Google uses a formula that incorporates amount bid, relevance of the ad's content to the keywords bid for, relevance of the landing page to the keywords bid on, and the click through rate of the ad to determine winning bids.
Natural Search
Search Engine Results that are driven by the search engines' ranking algorithm. This contrasts with paid search results that are generally determined by a bidding system. Natural search results are visually separated from paid search results in all of the major search engines.
Anchor text
The visible text of a hyperlink. It's often underlined or has some other visual clue that the text is a hyperlink. This text is used by search engines to help determine the content of the page being linked to and it factors into the ranking of the linked page. From a linkbuilding standpoint, you want links to your site to contain important keywords. If your site sells pancakes, example A is a much better a link than B if all else is equal. (The underlined text is the anchor text). Example A Click here for great tasting pancakes. Example B Click here for great tasting pancakes.
Search Engine Marketing
Search Engine Marketing is a broader term than either SEO or Paid Search that encompasses both.