Variacs have been used for ages......either to adjust the AC voltage to the amp's original specs, or just to "brown" the sound......more distortion. Eddie Van Halen was noted for doing this back in the day.
The Brown Box manufacturer is referring to AC wattage consumption (amps x volts = watts) of the amp. In the case of this device, it is limited to 5 amps of current.....which will handle most amplifiers.
A more rudimentary version of the Brown Box is a bucking transformer.....basically reduces the AC wall voltage down to something closer to the old voltage in years past. These have been used for years by tube hi-fi guys. A major benefit of using one of these devices is to lower the secondary voltages coming from the power transformer so that the voltage rating of the filter capacitors are not exceeded.....and the filtered DC voltages fed to the plates of the tubes, are closer to the original design. Lots of schematics for these on the interweb, but not for amateurs!
For tube rectified amps, one can substitute for a less efficient rectifier that has more voltage drop....thus reducing the secondary voltage fed to the power supply and tubes. But need to be sure the rectifier tube does not exceed the current capacity of the amp's power transformer.
