There is some significance to the amount claimed, but not much and mostly at the low end.
The existence of some damages caused by wrongful conduct is an element of some, but not all, claims for relief in lawsuits.
In some courts, the amount claimed in a complaint determines the filing fee for the complaint filed.
Limited jurisdiction courts usually cap the amount of relief that can be obtained in that forum, and a counterclaim in excess of that amount often results in the removal of a case to a forum with jurisdiction over the counterclaim.
Diversity jurisdiction in federal court requires an amount in controversy in excess of $75,000.
Class action cases seeking more than $5,000,000 (for the class as a whole) must be brought in federal court unless all plaintiffs and all defendants are from the same state.
Sometimes simplified rules of procedure are inapplicable to cases in excess of a specified amount in controversy. For example, in Colorado cases brought in its trial courts of general jurisdiction, simplified civil procedure rules apply if the amount in controversy is less than $100,000.
The federal rules of civil procedure and most state rules of civil procedure require "special damages" to be pleaded with specificity in the complaint to be recovered. There are several definitions of this term that are used. One of them is that: "In contract law, special damages (also called consequential damages) refer to irregular damages such as physical injuries during a breach of contract, but general damages would refer to the damages expected from the contract being breached."
In most cases, a default judgment which is entered because a defendant fails to respond to a complaint filed in court and duly served upon a defendant over which it has jurisdiction may not exceed the amount claimed in the complaint. The complaint can't be amended to claim more damages after it is filed and served. This requirement arguably has constitutional due process dimensions.
In arbitration under the American Arbitration Association's rules, certain cases to which other arbitration rules do not apply are presumptively subject to the AAA Commercial Rules if the amount in controversy is in excess of $500,000.
In cases where a defendant has both primary liability insurance and also "excess" or "umbrella" insurance, a claim in excess of the limits of insurance under the primary liability insurance policy immediately trigger the involvement of the excess or umbrella insurer.
The amount of damages claimed in a lawsuit is one important factor in determining whether a lawsuit has to be disclosed in the public disclosures of a publicly held company, or in the prospectus to an initial public offering of securities in a company, or in a private sale of the securities of a closely held company in a private placement memorandum.
The amount of damages claimed in a lawsuit is generally the initial value of the claim of the person bringing the lawsuit in a bankruptcy filed by the defendant unless and until the value of the claim is challenged in the bankruptcy court process.
The amount of damages claimed in a lawsuit is one factor to be considered in whether a transfer of property from a defendant to a third-party for less than substantially equivalent value is a fraudulent transfer.
A claim of damages in a lawsuit made without reasonable factual support can be a basis upon which an attorney filing the lawsuit may be sanctioned for misconduct by the court in which the case in pending.
Also, some states, including Colorado, prohibit filing a claim for a specified dollar amount in many circumstances.
Some states, including Colorado, allow certain kinds of damages (e.g., punitive damages) to be requested only in an amended complaint filed after some information has been exchanged by the parties after the lawsuit is filed.