Certiorari (pronunciation: sər-sh(ē-)ə-ˈrer-ē, -ˈrär-ē, -ˈra-rē) is a legal term in Roman, English and American law referring to a type of writ seeking judicial review. Certiorari ("to be searched") is the present passive infinitive of Latin certioro, a contraction of certiorem facere ("to search, lit. to make certain"). Certioro was a highly technical term appearing only in jurisprudential Latin, most frequently in the works of Ulpian, who favored it over the facere form.

Roman Law
In English law, certiorari is a public law relief (i.e. something for which you ask the court in order to deal with an action of the Government, council or other (quasi)-governmental organisation). See judicial review and writ. An order of certiorari is given by a senior court to quash a decision of a lower court or other (quasi)-governmental organisation. The use of certiorari in the UK is declining, due to the changes to the remedies available for judicial review.
Historically, certiorari was a prerogative writ used to direct a lower court or tribunal to certify for review the "record" in the case.
After the 1999 Woolf Reforms it is more commonly known as a quashing order.

English law
Certiorari is available as an incidential remedy to the remedies of mandamus, prohibition or injunction in the High Court of Australia due to the effect of s75(v) of the Australian Constitution.

Australian Law