Kurtosis is a term used in probability theory and statistics that measures the "tailedness" (the extreme outlying values of a bell curve) of the probability distribution of a real-valued random variable. For non-mathematicians this seems like gobbledy-gook, but measuring kurtosis is a means of quantifying the occurrence of extreme outlying variables on a graph.
For instance, most of us are familiar with how IQ scores breakdown on a bell curve. With IQ scores the majority of scores run from 85-115, with 100 as the mean score. On either side of this score range the numbers continue to decrease both in quantity until at the extreme ends you have "profound" retardation (individuals who are unable to speak, feed themselves, walk, etc.). On the other end you find "extreme" geniuses. Both of these latter scores are extremely rare in their occurrence. Kurtosis is the statistical means of quantifying these extreme "outlier" scores over extremely large sample sizes.