The power unit is explained in the description.
Now the Electronics;
The amps from the lipo's are run trough a ESC and the ESC control's the brushless motor.
The ESC is controlled by the Arduino by reading the throttle switch.
The throttle is nothing more than a potentiometer with 3 connectors V+, signal and Gnd.
This signal is read by the Arduino and send's a PMW signal in proportion of the throttle position to the ESC.