Here are two definitions:
The writ of certiorari is the judicial resolution issued by a higher judicial body requesting another judicial body but lower certification of everything in judicial proceedings for further review by the higher body for the purpose of resolving the appeal.
It can be said that the recourse of certiorari before the Federal Supreme Court of the United States goes back to an old expression of common law that has the meaning of delivering documentation. In other words, the writ of certiorari is a process to seek judicial review and an order issued by a court that agrees to review.