What is arduino_debug.exe for IDE 1.5.6r2? After installing IDE 1.5.6r2, there are two .exe files, arduino_debug.exe and arduino.exe (which is same name as previously installed IDE 1.0.5).
Windows binaries can either be Window or Console applications. A Window application can NOT produce text output. Text output is the easiest way to gather error messages related to bugs.

Hence, arduino_debug.exe should be used by Windows users that have found a bug in the Arduino IDE and wish to contribute submitting an issue on github.