A writ of certiorari is a way to have a higher court review the outcome of a lower court's proceedings. The word 'certioari' means "to be more fully informed". In this sense, a writ of cetiorari orders a lower court to deliver its record in a case so the higher court may review it.
Often times, a writ of cetiorari is a last resort for a defendant to have his or her case reviewed when it does not qualify for an appeal.
These writs are usually held in higher scrutiny than appeals. Many times they are only granted if:
The case could have national significance
The writ might harmonize conflicting decisions in the federal Circuit courts or