Definintion of h-index:
"A scientist has index h if h of his/her Np papers have at least h citations each, and the other (Np − h) papers have no more than h citations each."
In other words, a scholar with an index of h has published h papers each of which has been cited in other papers at least h times. Thus, the h-index reflects both the number of publications and the number of citations per publication. The index is designed to improve upon simpler measures such as the total number of citations or publications. The index works properly only for comparing scientists working in the same field; citation conventions differ widely among different fields.