The XROTOR MICRO is an ESC, which means Electronic Speed Control. It is essentially the motor driver in a quadcopter. Most quadcopter use brushless motors, because they are more fitted for the fast speeds of the propeller. But brushless motors aren't as easy to drive as simple DC motors. The current through the different coils has to be commutated depending on the current speed of the motor. The ESC does this for you and takes a PWM wave as input, whose duty cycle marks the requested speed. 30A is the current specification for this ESC. For more information google brushless motor.
if it could be replaced by an arduino
Short answer: No.
Long answer: An ESC is a highly specialized device, which is very fast and drives high currents. It may be possible to build something like an ESC with an Arduino in it's heart, but this would be a dumb way to waste your time. The Arduino would be busy controlling the motor, so that it would not be able to do anything else. If you look at how many different peripherals the Arduino embodies, this is a total waste. Also the Arduino cannot drive these high currents by itself. You would have to add extra components to do this. If you are able to build this, it would be much bigger than a normal ESC.
All in all: If you aren't a crack in electronics and want to try this just for achieving, then you should simply buy an ESC for your drone project. Mostly Arduinos have vanished from modern drones, because there are many boards, that are better fitted for this.