We find ourselves conversing about link backs and their value often. Here I have copied a bit of info from Wikipedia on the topic. I think it does a good job of explaining a link back and the value of link backs to a site.
From Wikipedia, the free encyclopedia
Backlinks are incoming links to a website or web page. Inbound links were originally important (prior to the emergence of search engines) as a primary means of web navigation; today their significance lies in search engine optimization (SEO). The number of backlinks is one indication of the popularity or importance of that website or page (for example, this is used by Google to determine the PageRank of a webpage). Outside of SEO, the backlinks of a webpage may be of significant personal, cultural or semantic interest: they indicate who is paying attention to that page.
Search engine rankings
Search engines often use the number of backlinks that a website has as one of the most important factors for determining that website's search engine ranking, popularity and importance. Google's description of their PageRank system, for instance, notes that Google interprets a link from page A to page B as a vote, by page A, for page B.[2]
There are several factors that determine the value of a backlink. Backlinks from authoritative sites on a given topic are highly valuable.[3] If both sites have content geared toward the keyword topic, the backlink is considered relevant and believed to have strong influence on the search engine rankings of the webpage granted the backlink. A backlink represents a favorable 'editorial vote' for the receiving webpage from another granting webpage. Another important factor is the anchor text of the backlink. Anchor text is the descriptive labeling of the hyperlink as it appears on a webpage. Search engine bots (i.e., spiders, crawlers, etc.) examine the anchor text to evaluate how relevant it is to the content on a webpage. Anchor text and webpage content congruency are highly weighted in search engine results page (SERP) rankings of a webpage with respect to any given keyword query by a search engine user.