What is Controversy?

Legal Definition
In jurisprudence, a controversy differs from a case; while the latter includes all suits, criminal as well as civil, a controversy is a purely civil proceeding.

For example, the Case or Controversy Clause of Article Three of the United States Constitution (Section 2, Clause 1) states that "the judicial Power shall extend ... to Controversies to which the United States shall be a Party". This clause has been deemed to impose a requirement that United States federal courts are not permitted to hear cases that do not pose an actual controversy—that is, an actual dispute between adverse parties which is capable of being resolved by the court. In addition to setting out the scope of the jurisdiction of the federal judiciary, it also prohibits courts from issuing advisory opinions, or from hearing cases that are either unripe, meaning that the controversy has not arisen yet, or moot, meaning that the controversy has already been resolved.

Amount in controversy is a term in United States civil procedure to denote a requirement that persons seeking to bring a lawsuit in a particular court must be suing for a certain minimum amount before that court may hear the case.
-- Wikipedia
Legal Definition
The provisions of the U.S. Constitution setting out the powers of the Federal judiciary, define those powers in using two different but related words "cases" and "controversies". See U.S Constitution, Article III, section 2. In framing judicial authority these words also represent limits. The Federal Courts do not, under Article III, have the power to resolve legal questions that do not arise out of an actual dispute between real parties. In some states, by contrast, the highest courts have jurisdiction to hear and provide advisory opinions on questions submitted by the state legislature. A statute attempting to give such jurisdiction to the Federal courts would run into the Constitutionally based requirement of a "case" or "controversy". For examples of cases in which the Supreme Court has found this critical element lacking, see, e.g., Arizonans for Official English v. Arizona, 520 U.S. 43 (1997) and Renne v. Geary, 501 U.S. 312 (1991).

This basic limit on judicial power has led to more specific limiting doctrines, including: mootness, ripeness, and standing.
Legal Definition
A dispute arising between two or more persons. It differs from case, which includes all suits criminal as well as civil; whereas controversy is a civil and not a criminal proceeding. 2 Dall. R. 419, 431, 432; 1 Tuck. Bl. Com. App. 420, 421; Story, Const. 1668.

2. By the constitution of the United States the judicial power shall extend to controversies to which the United States shall be a party. Art. 2, 1. The meaning to be attached to the word controversy in the constitution , is that above given.
-- Bouviers Law Dictionary
Legal Definition
A litigated question; adversary proceeding in a court of law; a civil action or suit, either at law or in equity. Barber v. Kennedy, 18 Minn. 216 (Gil. 196); State v. Guinotte, 156 Mo. 513, 57 S. W. 281, 50 L. R. A. 787. It differs from "case," which includes all suits, criminal as well as civil; whereas "controversy" is a civil and not a criminal proceeding. Chisholm v. Georgia, 2 Dall. 419. 431. 482. 1 L. Ed. 440.
-- Black's Law Dictionary
Legal Definition
The claim of a litigant before a court for adjudication by regular proceedings established for protection and redress. See 154 U. S. 447, 38 L. Ed. 1047, 14 Sup. Ct. Rep. 1125.
-- Ballentine's Law Dictionary