The text that a user would click on to follow a link. In the case the link is an image the image alt attribute may act in the place of anchor text.
Search engines assume that your page is authoritative for the words that people include in links pointing at your site. When links occur naturally they typically have a wide array of anchor text combinations. Too much similar anchor text may be a considered a sign of manipulation, and thus discounted or filtered. Make sure when you are building links that you control that you try to mix up your anchor text.