A citation search reveals the number of times a particular article/author has been cited in other works (generally articles, but this depends on the database).
A citation search can also be useful when you are looking for a particular journal or year(s) of publication, but for general scholarship, the citation search is most often used to find the citation history of an article or author.
The concept of "citation indexing" was explained by Eugene Garfield in his paper, "The concept of citation indexing: A unique and innovative tool for navigating the research literature," in 1994. the following is a quote from Derek Price that Garfield uses to distinguish between a reference and a citation.
"It seems to me a great pity to waste a good technical term by using the words citation and reference interchangeably. I therefore propose and adopt the convention that if Paper R contains a bibliographic footnote using and describing Paper C, then R contains a reference to C, and C has a citation from R. The number of references a paper has is measured by the number of items in its bibliography as endnotes, footnotes, etc., while the number of citations a paper has is found by looking it up [in a] citation index and seeing how many other papers mention it." (qtd from Derek Price's Little Science, Big Science, p. 284)
Thus a work has a citation when it is used in another work.
A work has a reference when it uses other works.
When you have a particular work which you intend to use for your research:
You can consult the bibliographical information provided by that particular work. This is called "backward citation" or "citation mining."
You can consult a citation index for that particular work and discover what other works referenced that particular work. This is called "forward citation" or "citation searching."