Anchor Text is the visible, clickable text in a hyperlink. It is often blue and underlined, such as this link to the Unumbox homepage.
Search engines use external anchor text (text other pages use to link to your site) as a reflection of how other people view your page - and by extension, what your pages may be about. While website owners typically can't control how other sites link to theirs, “you can make sure that anchor text you use within your own site is useful, descriptive, and relevant.” (Source: Google)
If many sites think that a particular page is relevant for a given set of terms, that page can manage to rank well even if the terms don't appear in the text itself.