Heavy-tailed distributions have tails that are not exponentially bounded (eg, log-normal & Pareto [heavy right tail], & t [both]). For general questions about fat tails, use the [kurtosis] tag.
Heavy-tailed distributions are probability distributions whose tails are not exponentially bounded; that is, they have heavier tails than the exponential distribution. Examples are the log-normal and Pareto (heavy right tail) and t distributions (both tails heavy). These are distributions for which the moment generating function do not exist for positive argument t.
There are more details and discussion at Differences between heavy tail and fat tail distributions, and at wikipedia. See also Chapter XIII in Applied Probability and Queues.
