My textbook states that the advantages of the refractory period is that it means that action potentials are discrete and also that it results in signals only being able to pass one way, but provides no explanation. Could anyone explain why this is?
The axon is an uniformly excitable structure; if you would stimulate an axon electrically somewhere in the middle, an action potential would be generated in both directions. Hence, an axon in itself does not have directionality.
Nonetheless, under normal physiological conditions, an axon conveys action potentials from the dendritic region to the axon terminal, called anterograde signaling. The reverse direction, retrograde action potentials, normally do not occur because signals arising in the dendritic region travel unidirectionally to the terminal. The reason why an action potential travels unidirectionally is because of the refractory period. Because the refractory period will cause the part of the axon that just generated an action potential to become unresponsive, the traveling action potential cannot generate another action potential in the retrograde direction, because the only excitable region available is in the anterograde direction to the terminal (Fig. 1).
Fig. 1. Refractoriness. source: University of British Columbia
As an analogy, it's like a car driving across a road and throwing a temporary road block behind it that first has to be taken away before the road can be used again. This means that when a car leaves the parking lot and enters the road, it can never go back, because it throws up road blocks that prevent it to return the way it came.