Reciprocal linking is the practice of trading links with another website in an "I'll link to you if you link to me" sort of deal.
Search engines are generally wise to this practice and reciprocal links are not always seen as influential as links which are not reciprocal. Links should seldom be part of a deal between websites and if you can't get people to link to your content without giving them something in return perhaps your content needs revised.
It's inevitable that some links on every website will be reciprocal, but it's up to you to make sure that you have a good balance. Reciprocal links should be a small minority of your total link profile.