What do the minimum, first quartile, median, third quartile, and maximum of a box and whisker plot represent?

They each contribute to the box plot in different ways (see below).
A box and whisker plot is a method of displaying data and its distribution.
The minimum is the lowest value in the data set and the maximum is the highest value in the set. The is the number that falls right in the middle of all of the data points.
The third quartile (also called the upper quartile) is where 25% of the data lies above this point and 75% below it. The first quartile (or the lower quartile) is the point in the data distribution where 75% of the data is greater than this value and 25% fall below this point.