Having the exact same data format, down to the binary level. That is, two files that are binary compatible will have the same pattern of zeroes and ones in the data portion of the file. The file header, however, may be different.
The term is used most commonly to state that data files produced by one application are exactly the same as data files produced by another application. For example, many software companies now produce applications for Windows and the Macintosh that are binary compatible, which means that a file produced in a Windows environment is interchangeable with a file produced on a Macintosh. This avoids many of the conversion problems caused by importing and exporting data.