Input vs Operating voltage (Mini)

I just got a Mini and got the blink sketch uploaded (yay) and now I am trying to calculate the battery situation I will need for my main project.

Now, I read that the input voltage is 7-9V while the operating voltage is 5V. As I understand it, the input voltage is what is required for the Arduino to actually function while the operating voltage is what is used to measure and everything.

I must be misunderstanding something though since using the USBSerial, I am powering the Mini with only 5V which is 2V under the required input voltage..no? How does it run under the the minimum required input voltage?

7-9V input power voltage goes thru regulator to make 5V to operate from.
USB does not go thru regulator, and supplies the 5V to operate from.
I/O signals must not exceed 0-5V by more than 0.5V (-0.5, +5.5).

Terminilogy can be a little confusing re: input power vs input/output levels.

Ok so what would happen if I connected 6V (4AA batteries) to the 5V input of the Mini? Would that burn it out? The Mini doesn't have a Vcc pin, just a few 9V and 5V input voltage pins.

Promini has RAW, which is where 7-9V go, and
VCC which is where 5V goes (in or out). Is between A3 and Reset pin.
4AA: May exceed 6V for a while when fresh.
I use 3 AA, 4.5V, will still get reliable 16 MHz operation down to 3.8V and may not see issues as it drops a little lower even.
6V is awkward - little too high to use with out some drop (can add a silicon diode in series for 0.7V drop), and a little too low for the onboard regulator.

Sorry for the bit of thread necromancy but what would happen if I did throw 4 AA batteries into the 5V pin? Would it burn it out?

Edit: for clarity, I am using a standard Arduino Mini http://arduino.cc/en/Main/ArduinoBoardMini

shiznatix:
Sorry for the bit of thread necromancy but what would happen if I did throw 4 AA batteries into the 5V pin? Would it burn it out?

Maybe.

The output of AA batteries varies, it's hardly ever 1.5V. They only put out 1.5V when they're brand new and under no load. They quickly drop down to about 1.3V in use. They also have quite a high ESR so the voltage will drop if you draw a lot of current from them.

If your question is really: "What would happen if I did throw 6V into the 5V pin? Would it burn it out?" then the answer is "Yes".

Then would it be wise to connect the batteries to the +9V pin on the Arduino? I know that putting less than 5V into the +5V pin still works just fine (powered by 2AA batteries for hours without problem).

So, if something between 6 and 5 V is put into the +9V pin then would there be any problems that I might encounter? I just don't want to put it in without knowing for sure that it will be ok.

Put a diode in series with the battery, drop the voltage a little to get away from 6V. Datasheet says:

Maximum Operating Voltage ............................................ 6.0V *

*NOTICE: Stresses beyond those listed under “Absolute Maximum Ratings”
may cause permanent damage to the device. This is a stress rating only and
functional operation of the device at these or other conditions beyond those indicated in the
operational sections of this specification is not implied. Exposure to absolute maximum rating
conditions for extended periods may affect device reliability.

Going into the RAW pin, you need enough voltage for the regulator to work.
The regulator needs >=6V to make regulated 5V:
http://www.micrel.com/_PDF/mic5205.pdf
VIN = VOUT + 1V;