Aristotle has just distinguished between primary and secondary substance. In this part of the Categories he claims that all definitions and names are necessarily predicated of primary substances.
It is clear from what has been said that if something is said of a subject both its name and its definition are necessarily predicated of the subject. For example, man is said of a subject, the individual man, and the name is of course predicated (since you will be predicating man of the individual man), and also the definition of man will be predicated of the individual man (since the individual man is also a man). Thus both the name and the definition will be predicated of the subject. But as for things which are in a subject, in most cases neither the name nor the definition is predicated of the subject. In some cases there is nothing to prevent the name from being predicated of the subject, but it is impossible for the definition to be predicated. For example, white, which is in a subject (the body), is predicated of the subject- for a body is called white. But the definition of white will never be predicated of the body.
From what Aristotle has already discussed, we know that both names and definitions are necessarily predicated of primary substances. We know this because we know that predication of the genus and difference are both transitively said of primary substances. We can point at an individual man such as Aristotle and claim that he is a man. We can also claim that he is the definition of man. So both the name man and the definition of that name can both be predicated primary substances that are men. In general, the name and definition of the primary substance can both be predicated of that substance. That is always true, regardless of which primary substance we are speaking of. If we are speaking instead of what is in a subject, then this is not necessarily true. We can usually call a man white but we cannot speak of that man and claim that he is a color. So while we can sometimes call a primary substance by the name of something in it, we can never call by the definition of what is in it.
This takes Aristotles distinctions of the four ways that something can be predicated and applies it to the first way that something can be referred to. One of the ways not said of and not in the subject applies only to primary substance. Primary substance is one way to take substance itself.
Next, Aristotle expands on the relationship of primary substance to subjects that are not primary substances.