Head of SEO at http://www.thinketc.com says, “It is really helpful for the sites if we distinguish two major concepts carefully i.e. link relevance and link importance. One may get confuse while considering these factors as both might look the same thing to the less experienced web masters. But the fact is that both are total different concepts.”
In simple words, link important means - what all pages are linked with you and it does not involve keyword usage at all. The best example for this is Page Rank. Page Rank of a website depends upon how many pages are linked to a website. Link relevance totally depends upon the keywords, which have been used on the various linking pages. All the linking pages must have all or some keywords for which a website is optimized on the basis of traffic analysis reports. Here, the presence of concerned keyword in Meta Description is must. If the importance of two links based upon relevance is equal then higher SEO value would be scored for the link on the page which has more important and relevant information.
Recently numbers of websites lost their impressive page rank over the night all of sudden. SEO companies working with unethical SEO practices blamed the search engines but it was the web owner who suffered. Therefore, keep eyes upon the quality of links being developed by the SEO experts.