OK, I understand where you are coming from now. An electronic device like a FEZ will only use the amount of power that it designed to. In the case of just the FEX board itself that might be 50mA or so at 5 Volts or 250mW (guessing hi I’m sure). No matter how large (in capacity) a battery pack you hook to it, the FEZ board will only use ‘its’ amount of power.
Power = voltage applied * the current flowing in the circuit. (Think of this like your car engine where power is the combination or torque and RPM). So as in our example above: 50mA * 5V = 250milliWatts. Think of this as the amount of power the FEZ needs to operate.
The FEZ boards use linear voltage regulators, which regulate the output voltage to what the device requires from a given range of input voltages (like the 6-12V rating of the FEX power input). Linear regulators work great but have the quirk that while they regulate the output voltage to what is needed, the current passing through them is the same as what the device (FEZ) is drawing. So we have so ‘left over’ voltage that is being ‘dropped’ across the input of the voltage regulator. Just like when we figured out how much power the FEZ was using we can figure out how much power is being used by the regulator itself if we apply 12 volts to it (12V applied - 5V that FEZ needs = 5V left over).
P = 50mA * 7V = 350mW (more power being wasted as heat than what it takes to run the FEZ)
If we use six volts though it looks more like this
P = 50mA * 1V = 50mW (much cooler operation)