Reciprocal Linking refers to creating reciprocal link between two websites, i.e. it is created when a website 'A' links to website 'B' which in turn links to website 'A'. It is an agreement between two websites where each website is hyperlinked to another website.
It is usually done between the sites that provide related services or information. The purpose of reciprocal liking is to provide readers a quick access to the related sites and to boost search engine rankings of the sites.
The reciprocal links should be built between related websites otherwise it will irritate your users that will harm SEO of your site, e.g. A car wash and dent repair company in the same city may link each other sites to attract more customers.