Stephen King's "toolbox" is not a literal toolbox, although he begins this section by describing a real one. What he is saying is that you need a toolbox of the mind. And, as you would take care of real tools, keeping them clean and not letting them get rusty, as a writer you need to take care of your mental tools, too. As most toolboxes are designed with levels, King describes our minds as having levels, too.
What tools of the mind does a person need for writing on the top level? First, King says you need vocabulary in your mental toolbox. The more vocabulary you can "pack in," the better off you are (114). Also on the first level is grammar. King points out that good writers break grammar rules all the time, but they do need to know them in the first place. This is because without an understanding of the essential structure of the English language, we cannot communicate effectively when we write.
On the next level of King's toolbox are what King calls the "elements of style," which is also the title of a book he mentions frequently, by Strunk and White. King does not really define "style" all that well, but he also places "form" in the second level of the toolbox, and he does talk about form at great length, the idea that the structure of paragraphs and longer units is an important aspect of writing.
Once King fills the first two levels of his toolbox, he finishes by talking about "magic." It is not clear whether he intends to put this in the third level of the toolbox, because in the next sections of his book, he drops the toolbox metaphor.
A toolbox is a good metaphor for the writer, and I cannot resist adding something I think must be in one's toolbox: an interest in what you are writing about. Without that, the other tools aren't much good!