Anchor text is a word or a phrase which is used to create a hyperlink.
Example of HTML linking.
<a href="http://www.xyz.com">anchor text</a>
The phrase in red is the anchor text. This is very important for search engine optimization as indexing and search engines use to to understand what the page is all about. In order to retrieve contextual information and description of the page topic and popularity the algorithms analyse a number of anchor text besides the link itself.
In order to provide relevant results on SERPs search engines use the anchor extensively. Hence webmaster use popular anchor text for ranking but then this can be manipulated hence the importance of anchor as ranking factor has been diluted. Overuse of anchor for ranking can often result in penalisation or drop in ranking of a website being promoted.
As always keywords are used as anchor text by webmasters. Earlier they used same anchor text again and again to rank the site on that keyword. This does not work anymore. Hence it is better to use minimally naturally occurring words and phrases that describe the page well nothing more.
Search engines have factored hundreds of metrics in their ranking algorithm hence repeated use of anchor is bound to fail.
Contextual inform is deciphered using semantics or correlated words and phrases in anchor and surrounding content.
There are few types of anchor texts:
Exact Match is a phrase that is used after the URL naming. For example if the page is about "website promotion" than that becomes the exact matching phrase similarly "top website promotion" will turn into partial match. Brand names can also be used in hyperlink creation or the link can just be left naked with the linking world.