For a quad, two motors are rotating in one direction, the other two the other way. Each lifting 25% of the weight. Balanced. It increases the rotation rate on the pair rotating in one direction, and does a corresponding decrease on the other pair. Lift remains balanced (front right, and rear left are now perhaps lifting 30% of the weight each, while front left and rear right are now lifting 20% of the weight each), but the torque being delivered to the pair with the higher lift is now much more.
Same applies for a hex, or octo.
The one that gets complex is the tricopter. Here the third rotor is normally tilted by a servo to counteract it's torque, and this tilt is adjusted. Much more like a helicopter, except only 1/3rd the torque has to be 'balanced' by this, since the other two rotors counteract one another.
Seriously, 'just'. It is easy to underestimate just how much torque the lift motors involve....
Best Wishes