The value of the largest observation in the lowest 25% of a data set. 25% of the points in a data set are equal to or less than this value. It is also called the 'first quartile', 'lower quartile' or '25th percentile'.
The first quartile can be approximately calculated by placing the data points in ascending order and determining the median of the lower half of the data set, i.e. the median of the values below the true median. The true median of the data set is the second quartile.
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.