Is there a way to know the voltage fed to AREF inside our sketch?
Not directly, but if one was using the Aref pin as an external voltage source, but for some reason not sure what value was, if one had a known fixed voltage wired to one of the analog pins, say the 3.3vdc from the shield connector, then one could 'back' calculated the Aref voltage by the value of the known voltage wired to the analog pin. Kind of weird but doable. I in the past wrote a sketch that could 'measure' the actually voltage being supplied to the AVR's Vcc and Avcc pins by using the internal constant band-gap voltage as a measurement value rather then a reference voltage and therefore obtained the needed values to 'back' calculate the chips Vcc voltage. Handy for applications where you are powering the chip directly with battery voltage where the normal 'reference' voltage used by the A/D would slowly change as the battery discharges.
When we issue the command analogReference(EXTERNAL) what is it that takes place?
That depends on what your application is doing with the A/D functions. If your sketch is always going to utilize the same external referece the the command only needs to be made once, usually in the setup function. However if you are changing the reference used for measuring different analog pins then you need to issue a new analogReference statement prior to reading a pin that required a different reference from the other analog pins. That can be tricky for a couple of reasons. First that when changing analog references the first reading of a analog pin tends to be inaccurate due to mux switching of the reference voltage. One needs a few 'dummy' reads to get a stable and more accurate reading.
The second caution is a little complex as explaned below from the arduino reference on using analogReference with the Aref pin. One can cause damage to the chip if there is a external voltage wired to the Aref pin but switch to the internal voltage source which could cause high current to flow into the Aref pin. So advice on using real external voltages wired to the Aref pins is to be sure you understand the following safety points:
Don't use anything less than 0V or more than 5V for external reference voltage on the AREF pin! If you're using an external reference on the AREF pin, you must set the analog reference to EXTERNAL before calling analogRead(). Otherwise, you will short together the active reference voltage (internally generated) and the AREF pin, possibly damaging the microcontroller on your Arduino board.
Alternatively, you can connect the external reference voltage to the AREF pin through a 5K resistor, allowing you to switch between external and internal reference voltages. Note that the resistor will alter the voltage that gets used as the reference because there is an internal 32K resistor on the AREF pin. The two act as a voltage divider, so, for example, 2.5V applied through the resistor will yield 2.5 * 32 / (32 + 5) = ~2.2V at the AREF pin.