One of the most concise examples I have seen fairly recently is this one, regarding the Writ of Certiorari. A little bit of history; the writ of certiorari is one of what are generally known as the prerogative writs, (the primary being Certiorari, Habeus Corpus, Mandamus, Quo Warrento, Prohibition, and Procedendo) which were orders, issued by the Courts in the name of the Crown or Sovereign, commanding one of the sovereign’s statutory delegates (Individuals whose governmental authority derives from a specific section of law) to perform a certain task (or, of course, to refrain from performing a task).
The general history of prerogative writs can be covered elsewhere; suffice it to say that a writ of Certiorari issued by an appeals court commands a lower court to send it a case for review. Courts are broken down in a variety of ways, but one of those ways is via jurisdiction; courts of the first instance are courts in which a petitioner, known as a plaintiff, may file, whereas courts of appeal are courts where a petitioner, known as an appellant, may ask for review of a lower court’s decision.
The way that a court, as a rule, grants this review is by issuing what was often called a writ of certiorari. In the modern day, especially in American courts, the writ is often named something else; a writ of review, leave to appeal, or whatnot. Often, the denial of certiorari is entirely at the discretion of the court one is appealing to. (This is not always the case; there are a variety of areas where an appeal must be granted, of course, but there are always exceptions).
One of the places where laypeople feel so confused is on what conditions a court of appeal tends to issue a writ of certiorari. Often, they believe that the writ is issued because the higher court does not agree with the lower court or has found a flaw in it; conversely, they often generally believe that the denial of a writ of certiorari means that the appeals court agrees with the lower court or believes its judgment to be sound.
This is false in both instances; but to understand why, one has to refer to two elemental judicial principles. Stare Decisis is the Latin maxim “To stand by that which has been decided”, itself akin to the famous “Let sleeping dogs lie”. More practically, a lower court may not overturn the decision of a higher court (if a case similar to one that has been decided by a higher court comes before a lower court, the lower court must obey by the holdings of the higher court; this is called precedent) and that a court of the same level should not, unless there is a good reason, overturn what it has previously held. The second principle is that of deference- that a higher court should not overturn the decision of a court of first instance unless there has been a mistake made- specifically, it should not overturn the decision because it would have ruled a different way, so long as the process by which that judgment was arrived at was legitimate.
As a result, the denial of a writ of certiorari does not mean that a higher court agrees with a lower court; it may simply defer to the judgment of the lower court and decide that there are no substantive grounds for review. In the alternate, the granting of a writ of certiorari does not mean that a higher court disagrees with the lower court. It may simple believe that the process was flawed (but that the outcome was correct) or that review is necessary to standardize, via stare decisis, the judgments of a series of lower courts.
The best example of the latter reason is illustrated in the United States Federal Circuits; there are eleven of them (actually thirteen, but eleven primary geographic ones), and each covers a separate physical area; the first covers the north-east, the second covers the New York area, the third covers the Pennsylvania area, the forth the middle of the east coast, the fifth the south, and so on. As a result, and as a result of the wildly varying public policy and public perception differences between the areas of the circuits, it is relatively common that the circuits differ in opinion. One of the most important reasons for an appeal to the United States Supreme Court is so that the Supreme Court may standardize precedent across all the circuits.
As a result, the denial of certiorari is not exceptionally unusual, and "…imports no expression of opinion upon the merits of the case, as the bar has been told many times." (Missouri v. Jenkins, SCOTUS, 1995) 7500 petitioners, for example, ask the United States Supreme Court for certiorari each year- and the court grants it in only a hundred or so cases. Appeals courts are by necessity smaller than courts of first instance; were they to hear every decision, the process would drag out immeasurably. But they do serve an important purpose and a check against gross error by lower courts.