Whenever one thing is predicated of another as of a subject, all things said of what is predicated will be said of the subject also. For example, man is predicated of the individual man, and animal of man; so animal will be predicated of the individual man also—for the individual man is both a man and an animal.
Whenever we have a something is “said of” a subject, anything “said of” that predicate will also be “said of” the subject. For example, we can describe an individual person as being human, and humans are all animals. Therefore, that individual person is also an animal. This applies to all cases where something is said of a subject.
In modern terms, Aristotle claims that the “said of” relation is transitive. If X is said of Y, and Z is said of X, then Z is said of Y too. Since any noun can be a subject, this allows for a very wide range of claims. This is not the only issue with this passage. Aristotle is also implicitly claiming that the “said of” relation is one that applies to parts. So part of being human is being an animal, therefore, we can say of human beings that they are animals.
Aristotle continues by discussing how this applies to differences as well as genera.