Q:

Ceiling fan installation box

How do I tell if this is a box for a ceiling fan?  This is a 25 foot ceiling.  No idea if this is ceiling fan friendly or not.  

A:

Judging by the screw hole on the bottom, left side of the picture (labelled "fan") the box seems capable of holding a fan. 
Likewise, seeing two nylock nuts holding the box in is also a pretty good indication of a strong mount on the back side of this box. 
I would say it is probably safe to proceed mounting a fan in this box.