Answer:
A demurrer is otherwise known as Federal Rule of Civil Procedure 12(b)(6). If you file a demurrer, or a 12(b)(6) motion, you are saying that the case should be dismisses for failure to state a claim.
Most demurrers are filed when the current law doesn't make something illegal or if you can't sue a party for something.
For example, if I sued you for "looking at me funny", you could file a demurrer, because there is no law against looking at somebody funny.
Here is another example:
Alan hits bob with a stick. Bob sues charlie for battery. Charlie would file a demurrer because Bob's suit against Charlie would not work, because it was Alan, not charlie, who hit bob with a stick.