The Hirsch index is increasingly being used to compare research achievements, and it has been reported in Nature and discussed in the correspondence pages of Nature and the Nautilus blog.
Essentially, h is the number of papers that somebody has published that have been cited at least h times. So if you have a ranking of papers by citation numbers, you go down the list, rank number increases while citation number decreases. The last rank number which is equal to or smaller than the corresponding citation number is the h index.
I'm all in favour of the h-index as it has rewarded me
for doing nothing. I left research in 2000, when my
h-index (determined retrospectively) stood at 10.
Since then it has increased by one unit every year
without any input from me (not even self-citations)
and it is now 16, as you can see here.
But I think people whose career prospects depend on this kind of measure, should think very carefully about this ...