Kurtosis measures the "heaviness of the tails" of a distribution (in compared to a normal distribution). Kurtosis is positive if the tails are "heavier" then for a normal distribution, and negative if the tails are "lighter" than for a normal distribution. The normal distribution has kurtosis of zero.
Kurtosis characterizes the shape of a distribution - that is, its value does not depend on an arbitrary change of the scale and location of the distribution. For example, kurtosis of a sample (or population) of temperature values in Fahrenheit will not change if you transform the values to Celsius (the mean and the variance will, however, change).
To calculate the kurtosis of a sample:
i) subtract the mean from each value to get a set of deviations from the mean;
ii) divide each deviation by the standard deviation of all the deviations;
iii) average the 4th power of the deviations and subtract 3 from the result.