Refer to figure.
CRITICAL ENGINE

When one of the engines on a typical multi engine aircraft becomes inoperative, a thrust imbalance exists between the operative and inoperative sides of the aircraft => this causes several negative effects in addition to the loss of one engine’s thrust.
The engine failure will cause a decrease in thrust and an increase in drag on the side of the failed engine. Most significantly, there will be an immediate yawing moment towards the failed (dead) engine.
One of the factors influencing the yawing moment is the length of the thrust arm => distance from the CG to the thrust line of the operating engine.

• For a propeller aircraft the length of the thrust arm is determined by the asymmetric effect of the propeller. At a positive angle of attack and when viewed from the rear, the thrust line of a clockwise rotating propeller is displaced to the right of the engine centre line => because the down going blade generates more thrust than the up going blade. Therefore, if both engines rotate clockwise, the right engine will have a longer thrust arm than the left engine. Thus, if the left engine fails, the thrust of the right engine acts through a longer thrust arm and will give a bigger yawing moment. The critical engine is the engine, the failure of which would give the biggest yawing moment.