Jack Davis explains the concept of polychoric correlation:
In polychoric correlation, we don’t need to know or specify where the boundary between “good” and “very good” is, just that it exists. The distribution of the ordinal responses, along with the assumption that the latent values follow a normal distribution, is enough that the polychor() function in the polycor R package can do that for us. In most practical cases, you don’t even need to know where the cutoffs are, but they are useful for demonstration that the method works.
Polychoric correlation estimates the correlation between such latent variables as if you actually knew what those values were. In the examples given, we start with the latent variables and use cutoffs to set them into bins, and then use polychoric on the artificially binned data. In any practical use case, the latent data would be invisible to you, and the cutoffs would be determined by whoever designed the survey.
Read on for a demonstration of the process in R.