In a 3phase motor, the phases cause magnetic fields that are 120degees apart, so they rise and fall in a circular pattern. In a single phase motor, the magnetic fields are 180 degrees apart so they don't rotate, they oppose each other and the motor won't spin. But if it DOES start spinning, that will create a shift in the way the rotor reacts to the fields, so it will keep spinning. The trick then is to get it to start spinning in the first place. There are several ways of doing that, so there are several types of single phase motors. Without knowing what kind you have, you cannot know for absolute sure if, let alone how, it can be reversed.
So to that point, what 347sparky is referring to is one of the most common types of single phase motors, the Capacitor Start type. In that design, a "starting capacitor" is used to create a phase shift in a separate part of the windings, which delays the magnetic field in that winding and gives it that virtual rotation. The motor begins rotating, then like I said, it keeps rotating in that same direction. In that design, most mfrs who follow NEMA design standards will use a wiring number convention that says that wires 5 and 8 are connected to that capacitor circuit, so swapping them changes which set of windings get the delayed magnetic field, thus changing the initial rotation.
Unfortunately, this is not universally true for all 1phase motors. And even if they are the same type, not all motor mfrs use the same wiring number system. So his first statement, about it saying so on (or inside) the motor is the most important. If there are no instructions telling you HOW to make it reverse, you cannot assume it is even capable of being reversed. Many are not.