To keep things very simple, we'll assume that you already understand some basic principles such as thrust, drag, lift and gravity. Multicopters depend on the flight controller and ESCs to distribute the correct speed to each of the motors depending on what we want the aircraft to do. Using the quadcopter (four motor) multirotor as our example, this aircraft must have all four motors turning at the same speed to achieve smooth vertical take-offs and landings (assuming of course that the weight of the quadcopter is evenly distributed across the frame).
Pitch and roll rotation is controlled by increasing the speed of two motors on one side while slowing down the speed of the motors on the opposite side. For example, to roll left the motors on the right side of the frame must increase in speed and the motors on the left must decrease in speed. To roll to the right, the opposite must take place, the motors on the left side of the frame must increase in speed and the motors on the right must decrease at the same time.
In the same fashion, to roll forward (pitch) the two motors at the rear must increase in speed while the two motors at the front decrease and vice versa for a backward roll (pitch). In order for a quadcopter to fly forward the speed of the motors at the rear of the aircraft must be faster than the speed of the motors at the front which will cause the quadcopter to "lean" forward or roll around the pitch axis. Once in this position the quadcopter will fly forward when the speed of all four motors is increased, increasing the overall thrust. Generally, the greater the "lean" forward, the faster the quadcopter will travel. The same is true for travelling in reverse. To move backwards, the speed on the front motors must increase to cause the aircraft to "lean" backwards. Once the quadcopter is leaning backwards, the speed of all four motors is increased, increasing the overall thrust and the quadcopter flies backwards. Again, the greater the "lean" the faster it travels!
The quadcopter turns (aka yaw) to the left or right by increasing the speed of two motors that are diagonally across from one another. Thankfully, the flight controller and ESCs (electronic speed controllers) are responsible for increasing and decreasing the appropriate motors in response to the pilot's desires!
Clockwise and Counterclockwise Rotations
On a quadcopter (four motor) multirotor two motors diagonally across from one another must turn in one direction (clockwise) while the other two motors turn in the opposite direction (counterclockwise) in order to fly. This clockwise and counterclockwise "balance" is to alter the principle of cause and effect. For example, if all four motors were to turn in a clockwise rotation, the aircraft itself would also want to spin in a clockwise rotation because there is no tail fin(s) to help stabilize the aircraft. Likewise, if all four motors were to turn in a counterclockwise rotation, the quadcopter would also want to spin in that direction. To find the balance and achieve stable flight, the cause and effect of four motors turning in the same direction must be altered by having an equal number of opposite motors turning in the other direction.