The Hirsch number tries to quantify the (scientific) productivity of a scientist. The Hirsch number was first described by the physicist J.E. Hirsch in a 2005 PNAS paper: An index to quantify an individual’s scientific research output. Hirsch says:
I propose the index h, defined as the number of papers with citation number h, as a useful index to characterize the scientific output of a researcher.
Thus, in contrast to the widely used impact factor, the Hirsch number measures the productivity of an individual scientist and not the journal he publishes in. The Hirsch number tries to factor in both the number of papers and the number of citations of these papers.
Your personal Hirsch number should be equal or greater the number of years you have already spent in science. Again in contrast to the impact factor, you can calculate your Hirsch number with freely available tools. You can look up your papers in Google Scholar and write down the citations for each paper. Or, use online tools such as scHolar index to do the work for you.
Using a simple number to measure the productivity of scientist is a dangerous undertaking. But if numbers are needed (e.g. grant or job applications), the Hirsch number is a good tool. Widespread use of the Hirsch number could have broad implications, as authors would more carefully consider which journals would give them the highest number of citations.