Anchor text is the visible text in a hyperlink. Anchor text gets a lot of weight in search engine algorithms because the linked text is usually relevant to the landing page. The objective of search engines is to provide highly relevant search results; this is where anchor text helps as the tendency is, more often than not, to hyperlink words relevant to the landing page.
Usually this is exploited by webmasters to procure high results in SERPS (search engine results pages). The concept of Google Bombing was/is possible through anchor text manipulation. Much has been written on anchor text which is available on the web today.
Although the search engines are well aware of anchor text manipulation, not much change can be expected in the SE algorithms in the near future because the brighter side of the picture cannot be overlooked: anchor text delivers relevance.