Admission by demurrer

What does Admission by demurrer mean in American Law?

The definition of Admission by demurrer in the law of the United States, as defined by the lexicographer Arthur Leff in his legal dictionary is:

When one files a demurrer (or any otherwise named modern motion in the nature of a demurrer) what one is saying, in effect, is “even if everything he says in his pleading is true, I still ought to win.” That is, for purposes of the demurrer, everything properly pleaded is treated as if it were true. But if the demurrer is overruled, then the facts again become not admitted and must be proved, i.e., an “admission by demurrer” is neither a judicial admission nor an evidentiary admission:

The facts are as if they had never been admitted.