To climb an aircraft, you increase the wing angle of attack by raising the leading edge. Since the wing is rigidly attached to the airplane, you pitch the entire airplane nose up. Now the engine crankshaft is not parallel with the airflow; it's also pitched up with the front of the crank higher than the rear. The crankshaft tilt also tilts the propeller hub, so the propeller axis is no longer parallel to the air flowing past it. This causes the rising blade of the propeller to meet the air at a shallower angle, producing less thrust, while the falling blade of the propeller meets the air at a greater angle, producing more thrust.
Thus, the prop produces more thrust on one side of the aircraft than the other. In a single-engine plane, this tends to make it yaw, and rudder is used to counteract this. In a twin, if the props rotate in opposite directions, the effect cancels - until one engine fails. When that happens, you're better off if the plane is designed so that the high-thrust side is inboard of the engine, closer to the fuselage, rather than outboard. That requires having both props turn so they move inboard at the top of their arc (i.e. clockwise rotation on the left engine, CCW on the right engine).
Dave