What does the option "Enable Display field" shown when creating a new file field do/mean?
It will provide you an additional option whether you want to display the attached file or not. As you can see the description provide under that option in following image.


  


Now enabling it, will add check box option to content editing layer as you can see in following image.

Include file in display


  


So, if you check it will show the file in final display and if you uncheck it will not show the file. 

Hence, it provides one extra quick option to author whether they want to show the attached file or not other-wise previously they had to go back and delete entire file from the content and again if they want to put they have to again upload and insert. Here, it is like On-Off Switch.