Bibliometrics is a set of methods used to study new ways of understanding the scholarly communication process and the structure of science through citation relationships between journals, scholars and papers. Сommonly-used bibliometric methods are citation analysis and content analysis. The best known bibliometric databases are Google Scholar and Scopus, both of which use the H index to calculate the distribution of citations received by a given researcher's publications.
The concept of the H index (also known as the Hirsch number) was proposed by J.E. Hirsch in his paper ‘An index to quantify an individual's scientific research output’ in September 2005. The contemporary H index was proposed by Antonis Sidiropoulos, Dimitrios Katsaros and Yannis Manolopoulos in their paper ‘Generalised h-index for disclosing latent facts in citation networks’ one year later, in July 2006.
The H index attempts to measure both the scientific productivity and the apparent scientific impact of a scientist. It adds an age-related weighting to each cited article, giving less weight to older articles. The weighting is parametrised in a way that for an article published during the current year, its citations account four times. For an article published 4 years ago, its citations account only one time. For an article published 6 years ago, its citations account 4/6 times, and so on.
You can find more information about the H index at Wikipedia and about bibliometrics in general in this presentation (pdf, 1.7mb).