Section 2 is the meat of the book and includes a reference to the classes and their members. This is similar to the online API, but lacking the descriptions for the methods / classes. This is strictly a quick reference of the methods, their arguments, return types and modifiers, and the variables belonging to a class. For a description of every method, use the online API. Personally though, I find this reference quicker to use than the online API when searching for a particular class. It probably comes down to personal preference, though.
Sections 3 and 4 I honestly haven't found a need for. The first two sections alone are worth the (relatively) [inexpensive] price of the book.
For reference, my qualifications include Sun Java Programmer Certification 1.4 (Passed with an 86%), Graduated Magna Cum Laude from UMass Dartmouth with a Computer Science degree.
Part 3 contains topics on the transition of Java from 1.0 to its current incarnation, detailing deprecated classes, new classes, etc. Part 4 is the cross-reference section, where if you know the name of the method, but not the class that contains that method, you can simply look it up. There's much more than just methods, though; subclasses, descendants, fields, and "extended by"'s are also some of the details here.
This book is quite an impressive achievement, and I hope to get my hands on Volume 1 sometime soon.