The explanation of the rebus principle can be found on p. 220 of the paperback edition of the book.
A rebus is a sign that stands for or represents something. A rebus uses a pictorial symbol to represent all or part of a word. In linguistics, the rebus principle is the idea that a symbol can be used to represent a certain sound that is included in the word for that symbol.
On p. 220, Diamond explains this in the context of Sumerian writing. He says that it is very easy to draw a symbol to represent the word “arrow.” However, it is not simple to draw a symbol that would be easily understood to mean “life.” However, in Sumerian, both the word “arrow” and the word “life” are pronounced the same way. Thus, a rebus can be used. If you draw an arrow, it no longer just means “arrow.” Instead, it can mean either “arrow” or “life” because both are pronounced in the same way.
This principle is very important because it allows people to more easily write words for which it would be very hard to draw comprehensible symbols.