In the past, I've been unsure what Alan Kay meant whenever he talked about "late binding" being the key insight into the development of Smalltalk, an insight which he attributes to his reading of the Lisp 1.5 manual. I think what he's talking about is the idea that if you have some part of your program that contains a piece of data, but now you want the construction of that data to vary based on some particular condition of the dynamic execution of the program, wrap it in a procedure. Now you can dynamically generate the data instead of fixing it once and for all.
This is of course possible regardless of whether you're in an OO or FP framework; in the context of OO, he's referring to the idea that instead of a record with fixed fields, you use methods that dynamically return the values of the fields. In functional languages you can do the analogous thing by placing functions in the slots of records, or in general you can just replace any datatype α with (→ α).
You can also take this in arguably the wrong direction and base the dynamic generation of this data on the mutable state of the program (whether that's the mutable fields of the object the method belongs to, or the mutable state of variables in the closure of a procedure). So you can see how late binding could be seen as a gateway drug to overuse of mutation.
But more and more I appreciate the power and simplicity of this notion that the natural path a program follows as it gets more complex is to take the pieces that are fixed and abstract them; to take the constants and make them variable; to take variables and fields and turn them into procedures and methods.