Apart from a smoother & silent ride, synthetic Oil which is manufactured with specially designed formula, forms a very thin layer over piston and other engine parts.
Thinner layer means, lesser friction, lesser wear and tear of the engine thus increasing engine life.
Also, it helps to great extent in cold start conditions when mineral oil tends to become bit denser when cold.
Last one I know, is the effective lubrication it provides in bumper to bumper city traffic were the engine is strained much.