The h-index is a measure of "citedness" as a surrogate for productivity and impact. It is the number of articles h in a group of publications N that have received h or more citations. For example, an h-index of 20 means that there are 20 items in the selected group N that have received 20 or more citations. It is like a median, and useful because it discounts the disproportionate weight of highly cited and uncited papers that would skew a mean. However, the h-index will vary considerably depending on a person's number of credited publications and the length of time they've been active: older and more prolific authors will usually have higher h-indexes than younger or less prolific authors. If you want to compare your h-index to someone else's, you need to use the same methodology to calculate them and then normalize the values by dividing them by a second factor, e.g. years since PhD. The standard caveats apply when using h-indexes in personnel and funding decisions.
See also a more thorough method.