Well, "behaviour and state" is also incomplete, because it fails to mention anything about how you refer to parts of state and particular behaviours.
"a mapping of names to values and functions" on the other hand mentions both state ("values") and behaviour (functions) and also tells you that they have names.
> they've never learned a proper definition for it?
Well, there are many different valid definitions for objects, and even more for OO. There are people who don't know any of them for sure, but I strongly suspect that you've dismissed many good definitions as "vague, biased, incomplete" on the grounds of them not being your preferred one. You did it at least once just now, when you failed to realize that "a mapping of names to values and functions" is the same thing as "[named] behaviour and state".