Author impact metrics are meant to quantify a researcher's impact on the field on discipline in which they work. A straightforward way of measuring author impact is counting the number of articles, book chapters, or books they have created and the number of times these publications are cited by other researchers.
Additional metrics for measuring author impact have been devised. Below are a few examples of those metrics and a definition of how they are calculated.
Proposed by Jorge E. Hirsch, this is the most widely used author impact metric. Using this metric, an index of h means that your h most highly-cited articles have at least h citations each. For example, an author has 5 publications with citations of 10, 7, 5, 4, and 2. That author's h-index would be 4 because they have four articles with 4 citations or more citations. Note that an author's h-index cannot be larger than their total number of publications.
Proposed in 2006 by Leo Egghe as an alternative to the h-index, this metric attempts to quantify the impact of an author's most cited papers. Using this metric, an index of g means that an author's g most cited articles have at least g² total citations. For example, an author has 5 publications with citations of 10, 7, 5, 4, and 2. That author's g-index would be five because each time the author's citations are added together (10, 10+7, 10+7+5, 10+7+5+4, 10+7+5+4+2) the total is greater than the number of citations squared (1, 4, 9, 16, 25).
The i10 metric was developed by Google and is used only in Google Scholar. It is calculated based on the number of publications with at least 10 citations.