The h-index quantifies the number of articles published and weighs that against the the scientist's impact on the field. The h-index is based on the number of cited papers and the number of citations from other articles. Different mechanisms will provide different results (e.g. the difference in your impact factor when using ISI Web of Science vs. using Google to manually calculate). Your h-index should not include the number of self-citations.
When going up for promotion and tenure, you may want to calculate your h-index from Web of Science and Google to provide a more precise measure of your impact on the field.
See Citation Analysis for instructions to calculate your own h-index!