Buttered eggs was used as a term to describe two different cooked egg dishes, one of which nowadays we would probably just call “scrambled” eggs.
For the first, dish you beat eggs, then cooked them in a pot or frying pan with melted butter in it, stirring until thickened, and served them on buttered toast.
The second dish was chopped hard-boiled eggs reheated in a small pot with a small amount of cream, butter, and seasoning.
Buttered eggs is also the name of a technique for preserving eggs; see Buttered Eggs (1).