A reciprocal link is a mutual link between two objects, commonly between two websites to ensure mutual traffic. Example: Alice and Bob have websites. If Bob's website links to Alice's website, and Alice's website links to Bob's website, the websites are reciprocally linked. Website owners often submit their sites to reciprocal link exchange directories, in order to achieve higher rankings in the search engines. Reciprocal linking between websites is an important part of the search engine optimization process because Google uses link popularity algorithms (defined as the number of links that led to a particular page and the anchor text of the link) to rank websites for relevancy.
Relevant linking is a derivative of reciprocal linking in which a site linked to another site contains only content compatible and relevant to the linked site. Relevant linking has become increasingly important because most major search engines stress that -- in Google's words -- "quantity, quality, and relevance of links count towards your rating."
The engines' insistence on reciprocal links being relevant developed because many of the methods described below -- free-for-all linking, link doping, incestuous linking, overlinking, multi-way linking -- and other schemes were designed to unethically "fool" search-engines into awarding undeservedly high page ranks and/or return positions to sites engaged in search-engine spamming.