Relevant or quality links are simply links that were created with consideration of their usefulness or relationship with the content in which they appear. Links to your site on prominent, trustworthy sites can help you establish credibility, direct quality traffic your way, and even improve your search engine ranking.
Search engines consider the relevance of links to your site when evaluating their significance to your own site's value. Search engines may not put much stock in a link from your friend's online sock store to your hotel. But if the local Chamber of Commerce website links to your hotel from an article about great lodging in your area - well, that is a relevant link.
Relevant links can not only boost your search engine performance but also direct quality traffic to your site. Visitors to the Chamber of Commerce site's lodging area are already looking for a hotel, for example. A link to your site can bring them right to your door.