The g-index is calculated based on the distribution of citations received by a given researcher's publications, such that:
given a set of articles ranked in decreasing order of the number of citations that they received, the g-index is the unique largest number such that the top g articles received together at least g^{2} citations.
A g-index of 20 means that an academic has published at least 20 articles that combined have received at least 400 citations. However, unlike the h-index these citations could be generated by only a small number of articles. For instance an academic with 20 papers, 15 of which have no citations with the remaining five having respectively 350, 35, 10, 3 and 2 citations would have a g-index of 20, but a h-index of 3 (three papers with at least 3 citations each).
Roughly, h is the number of papers of a certain “quality” [citations] threshold, a threshold that rises as h rises; g allows citations from higher-cited papers to be used to bolster lower-cited papers in meeting this threshold. Therefore, in all cases g is at least h, and is in most cases higher. However, unlike the h-index, the g-index saturates whenever the average number of citations for all published papers exceeds the total number of published papers; the way it is defined, the g-index is not adapted to this situation.
Egghe, Leo (2006) Theory and practise of the g-index, Scientometrics, 69(1): 131–152. doi:10.1007/s11192-006-0144-7
Information taken from Harzing.com (Metrics: h and g-index)
g-index looks at overall record
g-index allows highly-cited papers to bolster low-cited papers
You can consult your g-index through Publish or Perish (free downloadable software for academic citations analysis)
Information taken from Harzing.com (Metrics: h and g-index)