The median is one of two measures of center of one quantitative variable in summary statistics.When numbers in a data set are ordered sequentially, the median is the middle value in the total list of numbers. For the rest of the values in the data set, this means half of the numbers lie above the middle value, and half lie below the middle value. This Virginia Tech website is a good resource for defining median, as well as other measures of center, while this website explains how to find the median in data sets with an even or odd number of values.
Both the mean and median are measures of center, but unlike the mean, the median is a good measure of center for a skewed data set because it is not influenced by outliers. For symmetric distributions, the median and mean are generally close enough to each other where either could be used as a good measure of center.
The College of Marin website is a good resource on the discussion between median and mean and which one is a better option for different distributions. The Platinum GMAT test preparation website, and Purple Math are additional resources for concise definitions of median with examples of data sets.
Care should be taken in the analysis of data where averages are used. Both mean and median can be used as the average of a data set, but unless otherwise stated, the average of a distribution is the mean. As discussed, the use of median or mean to describe the center of a distribution depend on the data set, outliers, and skewness.