Pate is a word used to refer to the actual inside of the cheese — what’s inside the rind or crust.
It’s only used in the context of cheeses that do develop a surface rind. You wouldn’t, for instance, use it to talk about Cream Cheese.
It is borrowed from the French word, pâte. Unfortunately, there really isn’t a good, generally accepted English word to use instead that will sum up this concept. Sometimes in English people will refer to it as the “paste” of a cheese, but that always sounds a bit forced.