What is Ad Quod Damnum?

Legal Definition
Ad quod damnum or ad damnum is a Latin phrase meaning "according to the harm" or "appropriate to the harm". It is used in tort law as a measure of damage inflicted, and implying a remedy, if one exists, ought to correspond specifically and only to the damage suffered. It is also used in pleading, as the statement of the plaintiff's money loss or damages claimed.

Most U.S. states prohibit plaintiffs from demanding a specific amount of money in the ad damnum section of a complaint initiating a civil action for personal injury or wrongful death. This is to prevent unethical attorneys from gaining undue publicity for their cases (and prejudicing the due process rights of defendants) by demanding outrageous amounts that they cannot possibly prove at trial. This is why such complaints simply demand "pecuniary loss" or "monetary damages in an amount according to proof." Of course, at some point the defendant needs to get some idea of what amount of money the plaintiff actually wants, so the defendant can usually serve interrogatories directed to that issue or a formal request for a statement of damages as part of the discovery process.

In theory, the other public policy choice besides muzzling attorneys would be to prevent journalists from reporting on legal complaints that they do not understand (e.g. by requiring them to undergo basic legal training), but such a licensing requirement would be a prior restraint in violation of the freedom of speech clause in the First Amendment to the United States Constitution.
-- Wikipedia
Legal Definition
The name of a writ formerly issuing from the English chancery, commanding the sheriff to make inquiry "in what damage" a specified act, If done, wlll tend. Ad quod damnum is a writ which ought to be sued before the king grants certain liberties, as a fair, market or such like, which may be prejudicial to others, and thereby it should be inquired whether it will be a prejudice to grant them, and to whom it will be prejudicial, and what prejudice will come thereby. There is also another writ of ad quod damnum, if any one will turn a common highway and lay out another way as beneficial. Termes de la Ley.
-- Black's Law Dictionary
Legal Definition
A writ under which a license from the king was obtained. See 2 Bl. Comm. 271.
-- Ballentine's Law Dictionary