A citation search is a search for other articles that have made reference to a particular book or article. A citation search will show you who has mentioned a particular article, where, and how many times.
Citation searching is also very useful if you are trying to trace the evolution of a scholarly idea or theory. When you find other works that have cited a particular work, you can see how the idea has been changed or added to over time.
Citation searching can also be useful if you have one relevant article but are having trouble finding others. Use the citations in your one relevant article to find the resources your article used. This is considered moving up the ancestry of a citation line, and it can often lead to new discoveries on your topic.
Some databases allow you to see citation information (e.g. JSTOR). Others will have citation links, allowing you to navigate by clicking on a citation that interests you and find more information.