What is Discretion?

Legal Definition
Discretion has the meaning of acting on one's own authority and judgement. In law, discretion as to legal rulings, such as whether evidence is excluded at a trial, may be exercised by a judge. Some view discretion negatively, while some view it positively. Discretion is at all levels of law enforcement.
-- Wikipedia
Legal Definition
Practice. When it is said that something is left to the discretion of a judge, it signifies that he ought to decide according to the rules of equity, and the nature of circumstances. Louis. Code, art. 3522, No. 13; 2 Inst. 50, 298; 4 Serg. & Rawle, 265; 3 Burr. 2539.

2. The discretion of a judge is said to be the law of tyrants; it is always unkown; it is different in different men; it is casual, and depends upon constitution, temper, and passion. In the best, it is oftentimes caprice; in the worst, it is every vice, folly, and passion, to which human nature is liable. Optima lex quae minimum relinquit arbitrio judicis: optimus judex qui minimum sibi. Bac. Aph; 1 Day's Cas.. 80, ii.; 1 Pow. Mortg. 247, a; 2 Supp. to Ves. Jr. 391; Toull. liv. 3, n. 338; 1 Lill. Ab. 447.

3. There is a species of discretion which is authorized by express law, and, without which, justice cannot be administered; for example, an old offender, a man of much intelligence and cunning, whose talents render him dangerous to the community, induces a young man of weak intellect to commit a larceny in company with himself; they are both liable to be punished for the offence. The law, foreseeing such a case, has provided that the punishment should be proportioned, so as to do justice, and it has left such apportionment to the discretion of the judge. It is evident that, without such discretion, justice could not be administered, for one of these parties assuredly deserves a much more severe punishment than the other.
-- Bouviers Law Dictionary
Legal Definition
Crim. law. The ability to know and distinguish between good and evil; between what is lawful and what is unlawful.

2. The age at which children are said to have discretion, is not very accurately ascertained. Under seven years, it seems that no circumstances of mischievous discretion can be admitted to overthrow the strong presumption of innocence, which is raised by an age so tender. 1 Hale, P. C. 27, 8; 4 Bl. Coin. 23. Between the ages of seven and fourteen, the infant is, prima facie, destitute of criminal design, but this presumption diminishes as the age increases, and even during this interval of youth, may be repelled by positive evidence of vicious intention; for tenderness of years will not excuse a maturity in crime, the maxim in these cases being, malitia supplet aetatem. At fourteen, children are said to have acquired legal discretion. 1 Hale, P. C. 25.
-- Bouviers Law Dictionary
Legal Definition
A liberty or privilege allowed to a judge, within the confines of right and justice, but independent of narrow and unbending rules of positive law, to decide and act in accordance with what is fair, equitable, and wholesome, as determined upon the peculiar circumstances of the case, and as discerned by his personal wisdom and experience, guided by the spirit, principles, and analogies of the law. Osborn v. United States Bank, 9 Wheat 866, 6 L. Ed. 204; Ex parte Chase, 48 Ala. 310; Lent v. Tillson, 140 U. S. 316, 11 Sup. Ch 825, 35 L. Ed. 419; State v. Cummings, 36 Mo. 278; Murray v. Buell, 74 Wis. 14, 41 N. W. 1010; Perry v. Sait Lake City Council, 7 Utah, 143, 25 Pan. 998, 11 L. RA. 446.

When applied to public functionaries, discretion means a power or right conferred upon them by law or acting officially in certain circumstances, according to the dictates of their own judgment and conscience, uncontrolled by the judgment or conscience of others. This discretion undoubtedly is to some extent regulated by usage, or, if the term is preferred, by fixed principles. But by this is to be understood nothing more than that the same court cannot, consistently with its own dignity, and with its character and duty of administering impartial justice, decide in different ways two cases in every respect exactly alike. The question of fact whether the two cases are alike in every color, circumstance, and feature is of necessity to be submitted to the judgment of some tribunal. Judges v. People, 18 Wend. (N. Y.) 79, 99.

Lord Coke defines judicial discretion to be "discernere per legem quid ait justum," to see what would be just according to the laws in the premises. It does not mean a wild self-willfulness, which may prompt to any and every act; but this judicial discretion is guided by the law, (see what the law declares upon a certain statement of facts, and then decide in accordance with the law so as to do substantial equity and justice. Faber v. Bruner, 13 Me,

True, it is a matter of discretion ; but then the discretion is not willful or arbitrary, but legal. And, although its exercise be not purely a matter of law, yet it "involves a matter of law or legal inference," in the language of the Code, and an appeal will lie. Lovinier v. Pearce, 70 N. C. 17L

In criminal law and the law of torts, It means the capacity to distinguish between what is right and wrong, lawful or unlawful, wise or foolish, sufficiently to render one amenable and responsible for hla acta. Towle v. State, 3 Fla. 214.
-- Black's Law Dictionary
Legal Definition
The exercise of the best of a court’s judgment upon the occasion calling for it. See 8 Wend. (N. Y.) 462, 24 Am. Dec. 46.
-- Ballentine's Law Dictionary