Ethics and epistemology. How do either or both of these relate to the Allegory of the Cave?
First, we should briefly mention what the allegory of the cave is.
The allegory of the cave is found in Plato's Republic 514-520. In this illustration, Plato is saying that the default mode of people is to see in shadows. It is as if people are chained down and forced only to look a wall, which receives shadows from the illumination of fire and moving object. So, what these people see are shadows and not reality for what it is. It is only through philosophy that a person can see truly.
Epistemologically speaking, the allegory of the cave implies that there are eternal forms that have an objective reality. So, for example, goodness is not a matter of opinion. There is a essence of goodness, which can be perceived through philosophy. This is what scholars call Platonic forms.
This is also related to ethics directly, because it is only when we truly know what something is that we can seek to do it. For example, what is justice? What is piety? What is courage? According to Plato, there are not matters of opinion or utility. They have an objective eternal basis. When we know the essence of something, then we are one step closer to living it, which is a vital part of ethics.