Anchor Text

Anchor text is highlighted words on a page that link to another web page or resource. Clicking on the text, called hypertext, loads the linked resource in the user's browser. Links are created using the Hypertext Mark-up Language's (HTML) anchor element:
   
This is a hyperlink

The hypertext is the text that occurs between the angle brackets. It would generally appear as: This is a hyperlink in a web browser such as Internet Explorer or Mozilla.
The word hypertext was coined by Ted Nelson who, in the 1960s designed the first ever hypertext system called project Xanadu. Nelson was inspired by a 1945 essay by Vanneva Bush titled: As We May Think. In it Bush envisaged a machine where the user could navigate a non-linear path through a trail of documents linked by concepts represented by words or phrases.

While anchor text tells a search engine nothing directly about the contents of the linked page it is used as a convenient heuristic. A heuristic is a rule of thumb that is normally effective in dealing with a given situation but does not absolutely guarantee the desired results. They are shortcuts where a much more detailed and complicated analysis would otherwise be necessary.

In this case the heuristic is to let humans evaluate the content of the target page. The anchor text should then represent in some way the contents of that page. You can think of it as a vote for your page with those keywords. In an ideal world it should be possible to build quite an effective search engine using anchor text alone. Indeed Oliver McBryan who first proposed the idea at the World Wide Web conference in 1994 used this method on his search engine, the WWW Worm.

There are a couple of pitfalls. Firstly many interesting and useful web pages don't have relevant inbound-links.  Secondly SEO experts can use this knowledge to subvert a search engine to favor their pages by creating inbound links for popular keyword from other sites under their control. This is a form of search engine spam.