As one may know from either middle school or high school, the median is the value in the middle of a sample. That is, there is an equal number of values less than and more than the median. However, if the amount in the sample is an even number, the median is the average of the two values in the middle. It is less affected by outliers and skewed data, so when the data is asymmetric it may be better to use the median instead of the mean. When data is skewed, the mean is probably not in the middle anymore and is no longer the best method of describing the center of distribution.
The reason for finding the median is usually for locating the center of distribution in a skewed graph.
There are some good descriptions of a median on both Wolfram and Dissertation-Statistics. This site also offers some good information, but you will have to search for it. A little searching on this site will provide you with more examples.