The direction of rotation of the propeller introduces an asymmetry which designers try to mitigate by adding more asymmetries. Specifically, a right-turning tractor propeller (clockwise from the pilot's viewpoint) will swirl the propeller wake in the same direction which adds a negative sideslip angle on the vertical tail (which sticks up into the upper half of the wake only). By pointing the axis of rotation of the propeller slightly to the right (right sidethrust), this sideslip angle can be reduced.
Other means of correction like an incidence on the vertical tail would not work equally well: Once the engine is throttled back, such an incidence would require to re-trim the aircraft. Still, siting in the prop wash, the effect scales with engine setting and helps to reduce the needed trim changes.
On multi-engined aircraft a sidethrust can help to reduce rudder input in engine-out cases. Here each wing engine points slightly away from the fuselage so its thrust will pull the aircraft into a helpful sideslip when the opposite engine has failed.
The propeller axis can also point slightly down in order to move the thrust line closer to the center of gravity, reducing thrust-related trim changes, and to reduce the P-factor effect (sideways shift of the thrust vector) at high angle of attack. This is called downthrust. One example would be the RR Griffon-engined version of the Supermarine Spitfire: When the new engine was installed, its lower thrust line required 2° more downthrust.
This is one of the few topics where the English version of Wikipedia stays schtum; only the German version has an article on it (Motorzug and Motorsturz).
