I hope this is a basic question

(I am at a basic level) and many thanks for trying to help me.
The Motor Shield R3 documentation states: Max current 2A per channel or 4A max (with external power supply)
and the stepper I have is 2.5A per phase 4.5V
Is the "external power supply" simply the external supply to the Arduino UNO board? Or is this the bit where it talks of cutting the pins etc?
For the sake of completeness the motor is an 8 wire hybrid that I hope to drive as a bipolar (serial or parralel) which becomes a 4 four wire motor. I will try using the stepper motor code from the Arduino Library.