Search engines use anchor text in the link to assign relevance. As search engine algorithms have gotten more advanced, they can also tell if the text surrounding the anchor text is relevant to A. the link itself and B. the destination page that the text links to. In other words: A search engine can detect if a link is so far off topic that there is no relevance and assign it a lower value than a link that is surrounded by related text and linking to. This practice came about recently as blogs became more popular and link spammers used blog comment boxes to spam useless comments laden with anchored links.
Why should you care?
If you are targeting certain key phrases, like all websites should be, you want to build links from other sites using your prime keywords as your anchor text. Let’s say I am the webmaster of The Real Estate Book’s site and I want to target the key phrase “homes for sale”. I would seek out high quality real estate related websites and try and get links that use Homes for Sale as my anchor text.