This is an action of a higher court of instructing a lower court to certify and submit an issue as having been decided below, and transmit that issue to the higher court so that the validity of the lower court holding may be determined.
A writ of certiorari is sometimes petitioned for during the course of a trial not yet completed, when a decision of the trial court is felt to potentially imminently result in manifest injustice. If the petition is granted, and the higher court issues a writ, then the lower court must often suspend proceedings until the issue is passed on by the higher court so that the trial can proceed in a fair manner and no prejudice is suffered by the moving party.
The United States Supreme Court generally issues writs of certiorari on cases coming from either a federal court of appeals, or a state supreme court. In certain cases, the Court will grant cert to cases directly from a federal district court. The circumstances in which this will occur are delineated by statute.
A petition for writ of certiorari will only be granted in cases where the higher court conceives that there is no other reasonable remedy at law, and both justice and judicial economy (as in obviating the need for a new trial) will be served.
Another meaning: In many court systems, certiorari is not an interlocutory appeal but one of a number of methods by which an appellate court can review the actions of a lower court or an administrative agency. The simplest distinction between certiorari and appeal (and nothing is ever simple in this atmosphere) is that cert is viewed as a discretionary right and appeal a mandatory right.