The h-index, or Hirsch index, is a bibliometric which measures the impact of an individual author.
It takes into account both the number of an individual's publications and their apparent impact on peers, as indicated by citation counts.
An author has an h-index of x if they have had x papers published, each of which has been cited more than x times. So to have an h-index of 20, 20 of your papers must have been cited at least 20 times:
Some bibliographic databases, such as Web of Science and Scopus, allow you to calculate a h-index score based on an author's published papers.