From AMS Glossary
One of a set of numbers (a quantile) on the random-variable axis that divides a probability distribution into four equal areas.
The three quartile points that lie between the extremes of the distribution are designated as Q1, Q2, Q3 and are defined in terms of the distribution function F(x) as follows:
Thus, Q2 coincides with the median. In empirical relative frequency tables, the quartiles are estimated by interpolation. The interquartile range 2Q is the distance from Q1 to Q3; half of this distance Q is called the semi-interquartile range (or quartile deviation) and is sometimes used as a crude measure of variability or spread.