According to this answer, found via a quick Google search...
Pearson correlation is a means of quantifying how much the mean and
expectation for two variables change simultaneously, if at all. In
other words, pearson correlation measures if two variables are moving
together, and to what degree.
You can’t apply this logic to categorical variables because there is
typically no order in categorical variables. For example, a variable
called “height” clearly places the observation of the human as
“larger” than that of a cat, because 1.75 metres is definitely larger
than 0.4 metres.
But the categories “human” and “feline” have no order, do they? Who
determines which is better than the other? Where is the value that we
use as the mean to calculate variance? Without order, it’s not
possible to correlate two variables.
But never fear, there are ways to find out if categorical variables
are related in some way; you need to simply move from correlation to
association. These would be tests such as Chi square and ANOVAs.
The response also points in the direction of this nice StackOverflow thread, which has some examples you may find helpful. I would point you to this thread, which gives a concise overview of "correlation" or relatedness tests. The comments sections in the thread will also point you in the right direction.