According to The University of Texas School of Information:
"Bibliometrics is a type of research method used in library and information science. It utilizes quantitative analysis and statistics to describe patterns of publication within a given field or body of literature. Researchers may use bibliometric methods of evaluation to determine the influence of a single writer, for example, or to describe the relationship between two or more writers or works."
Well, for all you librarians, I apologize for that boring rehash of a traumatic experience in your education. For the non-librarians out there, it can be pretty cool. Think of your favorite author. Now imagine you can trace back the impact that author has had on other authors, or the authors that impacted your favorite author. It becomes a cool web of information where you can find patterns where you might not have seen before. Science papers are probably the easiest to look at because those meticulous bastards write down everything and always want to top those that came before them.
Influences and sources can be seen to ripple through time, causing what we call "impact". Newton, Einstein, and Hawking would have crazy impact because their research is cited and used in most modern physics. A new author might not have a large impact, yet the journal they publish in would if the journal published other high impact articles and authors. It is all ripple effect and can be very interesting for the very patient and helpful for those looking for trends throughout the history of knowledge.