"The branch of library science concerned with the application of mathematical and statistical analysis to bibliography; the statistical analysis of books, articles, or other publications." (OED, Jan 2015)
Bibliometrics can help you to make decisions about where to publish your research and how to get information about the impact of published research. For example finding the highest Impact Journal in your Subject Area, or finding the most cited articles or finding out if you are being cited. It can also help you find current and future research collaborations.
Bibliometric tools can also help you increase the visibility of your research.
Bibliometrics is measuring impact not quality.
Article/Book Impact: The impact of particular works, such as journal articles, conference proceedings, and books, can be measured by the number of times they are cited by other works.
Journal impact: The impact of particular academic journals can be measured by the number of times their articles are cited and where they are cited.
Researcher impact: The number of works a researcher has published and the number of times these works have been cited can be an indicator for the impact of an individual researcher
Institutional impact: The prestige of a department or area of research within an institution can be measured by the collective impact of its individual researchers compared to those at other institutions.
Thanks to Michael Ladisch of UCD Library for giving me permission to use some of the content of his guide.