The H-index is a measure of scientific research output defined as the number h of publications that have been cited h times or more ( http://en.wikipedia.org/wiki/H-index). Thus an H-index of 10 indicates that 10 publications have been cited 10 times or more. The index is designed to improve upon simpler measures such as the total number of citations or publications to give a measure of both productivity and impact of published work. The index works properly only for comparing scientists working in the same field; citation conventions differ widely among different fields.
Google Scholar provides an estimate of the H-index as part of my Google Scholar Profile (http://scholar.google.ch/citations?user=qlhV1WcAAAAJ&hl=en). This is calculated by a computer program and may not be entirely accurate, you need at minimum to check that Google Scholar is correctly identifying your publications and not missing some or including works that are not yours.
The H-index increases with years of active publication and there have been proposals to adjust it by dividing by career-years to give a more comparative measure across researchers of different ages. However, its not always simple to define career-years, particularly for people who have had periods in and out of active research.
A few years ago, I noticed that my H-index was a not far off my age, and took some interest in watching to see whether it could overtake my age. Which it did about a year and half ago. My H-index is now 67 as at the time of this post, and in total my publications have received 44,003 citations. So maybe the new benchmark for H-index is to exceed your age.
JE Hirsch, the author of the h index estimated that after 20 years a “successful scientist” will have an h-index of 20, an “outstanding scientist” an h-index of 40, and a “truly unique” individual an h-index of 60a. However, he pointed out that values of h will vary between different fields. Well, I do appreciate confirmation that I am a truly unique individual, but suspect that apart from Google Scholar possibly estimating H on the high side, I am in a field (producing global health statistics) which by its nature will generate lots of citations. Helped along by the medical academics always wanting to provide a global context or a projection in the introductory paragraph of their paper on a particular disease.