Categorical propositions are class-inclusion claims
A categorical proposition is a claim about whether members of one class are included in, excluded from, or partially overlap with members of another class. When you say 'All cats are mammals,' you are asserting that the class of cats is entirely included within the class of mammals. When you say 'Some students are athletes,' you are asserting that at least one member of the class of students is also a member of the class of athletes. This class-based reading is the foundation of traditional logic and is the oldest formal system in the Western intellectual tradition.
Categorical logic treats each proposition as a relation between two classes, which is why it is sometimes called term logic or class logic. The power of the system comes from the fact that every categorical claim can be forced into one of just four standard forms, and those four forms support a small, memorable set of inferences. The price you pay is that you have to learn how to translate ordinary-language statements into standard form, and that translation is most of the early work in this unit.
Notice what categorical propositions do not do: they do not express conditional relationships ('if ... then'), they do not express degrees of probability, and they do not talk about individual named objects as such. The sentence 'Socrates is mortal' can be forced into categorical form only by treating 'Socrates' as a one-member class, which is a trick that works but obscures what categorical logic does best. Categorical logic shines when the subject and predicate both name genuine classes with multiple members: physicians, reptiles, prime numbers, licensed drivers. Keep the class-based reading front of mind as you work through the forms.