What is h-index?

The h-index is a number intended to represent both the productivity and impact of a particular scientist or scholar. 

The h-index is calculated by counting the number of publications for which an author has been cited by other authors at least that same number of times.  For instance, an h-index of 10 means that the scientist has published at least 10 papers that have each been cited at least 10 times.  If the scientist's 11th most cited publication was cited only 9 times, the h-index would remain at 10.  If the scientist's 11th most cited publication was cited 10 or more times, the h-index would rise to 10.

Part of the purpose of the h-index is to eliminate outlier publications that might give a skewed picture of a scientist's impact.  For instance, if a scientist published one paper many years ago, that was cited 8000 times but has since only published papers that have been cited 2 or 3 times each, a straight citation count for that scientist could make it seem that his or her long-term career work was very significant.  The h-index, however, would be much lower, signifying that the scientist's overall body of work was not necessarily as significant.

Where can you check your h-index or any other researcher's?
There are several databases that track the publications and their citations, including but not limited to Scopus,  Web of Science, and Google Scholar. Google Scholar is among the first options due to its speed for indexing and its free accessibility.