Relevance of links is important. It is best if the sites linking to and from you are related in theme (topics) to your site. A dog groomer could contact sites of veterinarians to see if they would like to exchange links. Everyone benefits from this type of exchange.
Back to the question of link popularity - simply stated it about "being connected" the more connected you are (you to others and other to you) the greater chance you will rank without any real effort at all. It can be very beneficial to develop early on as a hub or pointing to as many highly relevant and quality sites first (very easy to develop by yourself) this way as you commence developing incoming links other site owners will view your aggregation of quality links (and information) as highly desirable to link to.