In the law, "moot" is a term of art, and a moot issue is one which is not capable of judicial resolution because the controversy no longer presents a matter for which there is a remedy. A court will dismiss a case if the issue it presents is moot. I suspect that the use of "moot point" in everyday parlance stems from the legal meaning.
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An example of a moot case: a pregnant young girl seeks to have an abortion, and under the laws of the state she must have the consent of her parents to undergo the procedure or must obtain the permission of the court based upon a showing of psychological or medical necessity. The parents refuse consent, and she commences an action in court to obtain judicial approval. Based on the evidence presented, the court determines that there is an insufficient showing of necessity under the statutory standards, and also refuses permission. The girl appeals. While the trial and appellate proceedings have occurred, of course, her pregnancy has progressed, and by the time the appellate court hears the controversy, she has already given birth. At that point, the appellate court is liable to dismiss the appeal on the basis that the issue is moot, ie, no longer capable of remedy because there is no abortion to perform.
