Categorial grammar is a way of talking about the words and phrases that make up sentences. It explains how different parts of sentences fit together to make meaning. For example, let's take the sentence "The cat meowed." In this sentence, "the cat" is the subject and "meowed" is the verb - they are both types of parts of speech. Categorial grammar helps us understand how these two parts fit together to mean that the cat made a meow sound.