When analyzing ordinal data what is the median and going to tell me about my results?

It really depends on what the data is, the type of distribution and your purpose in collecting the data. It might well be the median is of no particular interest. The key thing is there are as many samples above as below the median. So for instance, If you are giving vaccinations by age, when you get to the median you are half way through.

The median is useful when you have can data with large outliers.  If you merely average the data, the average can be well outside the range of most of your data, while the median is more representative of what could be considered normal.

So, for example if you lived in a small town with 100 people,  99 of who had incomes between 0 and $50000, and one guy who won $100,000,000 in the lottery, the average income would be over a million, but the median income would be somewhere between 0 and $50000.  Which one seems more reasonable?