but why not,
what's wrong with connecting the motor directly to the arduino (with diodes)?
You destroy the microcontroller in the Arduino, either fully or "just" one (or more) I/O pins.
and what does the motor controller do exactly(how does it generally works?
It takes a low current in and gives a higher current out.
sorry not motor controller but motor driver(is there a difference?)
A motor driver is just a current amplifier, while a motor controller implies that there's some kind of logic circuitry (perhaps a microcontroller) involved, but sometimes they get mixed up.
Please use "Modify" rather than serial posting!
And please start reading some basic electronics tutorials (Google is your friend) - you'd be able to answer most of your questions here yourself with just a little bit of reading.