What is the h-index?
H-index stands for Hirsch index. It is a measure of an individual's scientific research output.
It was originally proposed by J.E. Hirsch.
If your h-index is 5, it means that you have 5 articles that have been cited at least 5 times.
However, one should also cite the source from which the h-index was derived, as in: "My h-index is 12, calculated on June 27, 2015, using Web of Science data from 1975-2015."
Hirsch believed the h-index was a better measure than one's "average citation rate." Hirsch used Web of Science as the tool for his calculations.
See: Hirsch, J. E. (2005). An Index to Quantify an Individual's Scientific Research Output. Proceedings Of The National Academy Of Sciences Of The United States Of America, 102(46), 16569-16572.