The value of the smallest observation in the highest 25% of a data set. 75% of the points in a data set are equal to or less than this value. It is also called the 'third' or 'upper' quartile of the dataset.
There are three quartiles, dividing the data set into four equal parts. They are shown below for a data set with 10 values: 49, 15, 3, 51, 12, 26, 60, 12, 17, 7.
The distance between the third (upper) and first (lower) quartiles is called the Inter-Quartile Range (IQR). The IQR is represented by the 'box' in a boxplot.