A CFI binder is a collection of lesson plans a Certified Flight Instructor (CFI) has which includes all their knowledge, notes, references, and so forth. Their CFI binder is how they teach. A properly set up CFI binder will allow a CFI to quickly prepare for any given lesson my containing condensed information on the subject at hand. This will allow the CFI to rapidly revision the subject prior to teaching it, as well as use it during a lesson.
A properly structured CFI binder will contain lesson plans that work as outlines of the lessons taught. They can therefore be relied upon during a lesson, and they can be useful to read through by student pilots after the lesson has been taught.