A helicopter with it's main roter blade turning will try to turn the body of the aircraft in the opposite direction to the blades. A tail rotor is used to balance this force.
If power to the blades is increased then this force is increased and the tail rotor must produce more force to counteract the increased tendency of the body to turn in the opposite direction to the blades.
This effect is most noticeable at low speed.
In a tricycle aeroplane, the same thisg occurs with the propeller. Thus when the power to the prop is increased, the reaction is for the fuselage to rotate the opposite way. This again is most noticeable when sitting on the runway.
If the prop rotates clockwise as seen from the cockpit then the fuselage will try to twist anti-clockwise. This paces extra downforce on the left wheel. This extra downforce will tend to make the aircraft turn to the left unless this movement is opposed by the use of rudder (steering).
The prop generates a corkscrew airflow which hits the fin at an angle of attack. This in the case of a clockwise prop will make the fin want to "fly to the right". Thus the nose will move to the left. When designing the aircraft, the designer ensures that this tendency is removed at cruise speed and power.
At slow speed and high power, extra right rudder is required to counteract this movement. Thus when in the climb or during the take-off roll, extra rudder input is required to keep the ball in the middle (aircraft running striaght).
In a twin, the engines will not normally be placed in front of the rudder. Thus the corkscrew airflow will have no effect.
Hope that covers it in non technical jargon.
DFC