A reciprocal link between two websites is simply a situation where the sites both link to each other. For example a property site in Philadelphia, PA might link to their sister office in Southampton, PA and vice versa.
Some linking arrangements, such as the above are natural and can give a boost to search engine rankings as links from other related/relevant or authority sites (as well as to a lesser extent links generally) are still the major ranking factor used by search engines. Other examples of natural results might be two Accountants in different cities who are specialists in the same unusual part of tax law who meet at a conference and link to each other as local experts in their field.
Some less natural approaches to building reciprocal links have been popular since the advent of links being used to determine rankings in the search engines. Some automated schemes exist where sites can join and request links from other sites. In some industries members were encouraged to improve their rankings through mass reciprocal link schemes – for example in the real estate industry. Major search engines are keen to determine the links which are more natural and those which are attempts to mass manipulate their results so it’s important not to overdo any reciprocal linking and to try to consider sites and partners which offer genuine value to your end users.