Definition 3.6 says that a positive integer is composite provided there is an integer b such that 1 < b < a and b |a. But the textbook's glossary defines a composite number as "a positive integer equal to the product of two smaller positive integers."
To equate these two definitions, suppose that a is a positive integer and consider the following three statements:
There exists an integer b such that 1 < b < a and b |a (the condition from Definition 3.6)