Anchor text is a clickable word or sentence with a hyperlink. It is generally underlined and in a different color than the body copy in order to be more noticeable and encourage the user to click on it.
When a user clicks through, he is taken to another web page (on the same site or on another site). Search engines (namely Google) takes into account anchor text as well as the hyperlink in order to determine a website's topic.
In this example phrase Catch the best expired domain names with Youdot, the anchor text is "Youdot"