A median is the central point of data arranged on a scale of some sort, oftentimes a scale of numbers. For example, the median of this set of numbers {2,5,10} is 5. Finding the median means finding the center value of all of the values present.
If there is an even number of values, then the average of the two center values is calculated. Open-ended questions do not provide answers that can be easily compared evenly on a scale, therefore making that a disadvantage of using a median.