Citation analysis involves examining an item's referring documents. It is used in searching for materials and analyzing their merit.
Suppose you've just read a 1992 journal article on blindsight and wish to learn more. One way would be to look at its bibliography for related writings. However, this would only obtain works written before your article. A fresher reading list would be the items published after 1992 that include your article in their references.
A citation index such as ISI's Web of Science can give you such a list. Citation indexes are databases of documents and their citations. They allow you to search forward in time from a known article to more recent publications on (more often than not) the same topic. Other citation indexes of scholarly publications include NASA's Astrophysics Data System, eprints.org, and the NEC Research Institute's ResearchIndex.
Data from citation indexes can be analyzed to determine the popularity and impact of specific articles, authors, and publications. Using citation analysis to gauge the importance of one's work, for example, is a significant part of the tenure review process (see Make Tenure Fast). Information scientists also use citation analysis to quantitatively assess the core journal titles and watershed publications in particular disciplines; interrelationships between authors from different institutions and schools of thought; and related data about the sociology of academia.
Although citation analysis is nothing new (the Science Citation Index began publication in 1961), greater computing power is making it more useful and widespread. Google's I'm Feeling Lucky feature and results ranking work with uncanny accuracy because they use citation analysis. They call it PageRank, but it is the same thing, just with hyperlinks instead of article references.
Google examines links within pages, and what words they use (the text within the anchor tags). The more popular a page is (the more it is linked to), the higher it will appear in the results list for a search of the words the links use. For example, several pages on the web link to Operation Clambake with a link titled Scientology. This is partially why Operation Clambake is currently the #1 result of a "Scientology" Google search.
Link popularity isn't the only criteria that Google measures when ranking search results. The popularity of the referring pages is also a factor (see hubs and authorities algorithm), as of course is the contents of the actual page. Web pages that contain similar links, and pages that are both linked to from other pages, have a greater chance of appearing together in Google's "similar pages" feature.
PageRank is not perfect. Thanks to stale pages, at the time this writing, Google's #1 result for "Bill Clinton" is whitehouse.gov. Google Bombs can also throw off accurate search results. Yet Google's ranking methods have proven more reliable than solely counting on possibly spammed text and keyword jamming.
E2 uses citation analysis to render lists of related nodes. Each node has a unique identification number. Whenever you move from one node to another, a vote is cast for a link between the two nodes (note the &lastnode_id= in the URL). For example, I was looking at a node about the philosophy of simplicity right before creating this node, so you see it in the list below. If you click on any of the links below, they will eventually move up the list. This system is why links to some nodes such as MR.T AT The Node Linked to All Others appear in several places (feel free to play with the system a little, but try not to disrupt its usefulness too much).
See also:
200 Years of Information
http://www.isinet.com/isi/hot/essays/citationindexing/21.html
http://www7.scu.edu.au/programme/fullpapers/1921/com1921.htm
http://www.tk421.net/essays/babel.shtml
Analysis of Everything
Semantic Web