In general the axis of the propeller will be inclined upwards to the direction of flight due to the angle of attack of the aircraft.
This causes the down moving blade to have a greater effective angle of attack than the up going blade and therefore to develop a greater thrust.
The difference in thrust on the two sides of the propeller disc causes a yawing moment. For a right hand propeller in a nose-up attitude the yaw will be to the left.
A similar effect can occur if the aeroplane is flying yawed, the asymmetry of the thrust causing a pitching moment is this case. The ratio of total blade area to the disc area, the greater the solidity the more power can be absorbed by the propeller.