Anchor text is the visible, clickable text in a hyperlink. For example, in the following link the target URL is "www.example.com", and the anchor text is "Good Website":
Anchor text is of especial importance to SEO, since search engines weigh the words in link anchor text heavily in determining relevancy. Having your targeted keywords in anchor text will typically help your rankings for these words. This is why "click here" is generally considered to be very poor anchor text.
However, caution should be used as search engines are aware that many SEOs try to abuse this, and have begun to penalize sites that try to intentionally manipulate search engine rankings by building keyword-rich anchor text links throughout the web.