As science became professionalized and scientific literature burgeoned, the question inevitably arose: how do we rank the quality of scientific journals, e.g. for purposes of tenure decisions, or to measure the influence of a particular journal, or to help researchers decide in what journals to publish?
The most influential metric of journal quality is the so called "impact factor", which Eugene Garfield mentioned in the journal Science in 1955. Lehigh's library provides access to impact factors via the online Journal Citation Reports (JCR), available from the database list at http://library.lehigh.edu/content/database_finder According to JCR, "The journal Impact Factor is the average number of times articles from the journal published in the past two years have been cited in the JCR year ['each JCR year contains one year of citation data']. The Impact Factor is calculated by dividing the number of citations in the JCR year by the total number of articles published in the two previous years. An Impact Factor of 1.0 means that, on average, the articles published one or two years ago have been cited one time. An Impact Factor of 2.5 means that, on average, the articles published one or two year ago have been cited two and a half times."
"Impact factors" have been criticized for many reasons but are still tremendously influential. Journals vie to outdo each other to achieve a high impact factor.
In addition to assessing the research impact of a specific journal, there are various ways to assess the research impact of a single researcher. If a research paper receives a high count, this may (though not necessarily) indicate a paper that has helped advance science. The producers of Web of Science, another library database, use citation and impact data to identify candidates for the Nobel Prize. 
A fun metric for mathematicians, which can be computed on MathSciNet (another of the Lehigh library's databases), is the "collaboration distance" from the famous mathematician Paul Erdos. According to MathSciNet, "collaboration distance finds a shortest publications-path between two authors".