The Collaborative International Dictionary of English v.0.48:

Certiorari \Cer`ti*o*ra"ri\, n. [So named from the emphatic word
   certiorari in the Latin form of the writ, which read
   certiorar volumus we wish to be certified.] (Law)
   A writ issuing out of chancery, or a superior court, to call
   up the records of a inferior court, or remove a cause there
   depending, in order that the party may have more sure and
   speedy justice, or that errors and irregularities may be
   corrected. It is obtained upon complaint of a party that he
   has not received justice, or can not have an impartial trial
   in the inferior court.
   [1913 Webster]

   Note: A certiorari is the correct process to remove the
         proceedings of a court in which cases are tried in a
         manner different from the course of the common law, as
         of county commissioners. It is also used as an
         auxiliary process in order to obtain a full return to
         some other process. --Bouvier.
         [1913 Webster]

WordNet (r) 3.0 (2006):

certiorari
    n 1: a common law writ issued by a superior court to one of
         inferior jurisdiction demanding the record of a particular
         case [syn: certiorari, writ of certiorari]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

CERTIORARI, practice. To be certified of; to be informed of. This is the
name of a writ issued from a superior court directed to one of inferior
jurisdiction, commanding the latter to certify and return to the former, the
record in the particular case. Bac. Ab. h.t.; 4 Vin. Ab. 330; Nels. Ab.
h.t.; Dane's Ab. Index, h.t.; 3 Penna. R. 24. A certiorari differs from a
writ of error. There is a distinction also between a hab. corp. and a
certiorari. The certiorari removes the cause; the hab. corp. only supersedes
the proceedings in below. 2 Lord Ray. 1102.
     2. By the common law, a supreme court has power to review the
proceedings of all inferior tribunals, and to pass upon their jurisdiction
and decisions on questions of law. But in general, the determination of such
inferior courts on questions of fact are conclusive, and cannot be reversed
on certiorari, unless some statute confers the power on such supreme court.
6 Wend. 564; 10 Pick. 358; 4 Halst. 209. When any error has occurred in the
proceedings of the court below, different from the course of the common law,
in any stage of the cause, either civil or criminal cases, the writ of
certiorari is the only remedy to correct such error, unless some other
statutory remedy has been given. 5 Binn. 27; 1 Gill & John. 196; 2 Mass. R.
245; 11 Mass. R. 466; 2 Virg. Cas. 270; 3 Halst. 123; 3 Pick. 194 4 Hayw.
100; 2 Greenl. 165; 8 Greenl. 293. A certiorari, for example, is the correct
process to remove the proceedings of a court of sessions, or of county
commissioners in laying out highways. 2 Binn. 250 2 Mass. 249; 7 Mass. 158;
8 Pick. 440 13 Pick. 195; 1 Overt. 131; 2 Overt. 109; 2 Pen. 1038; 8 Verm.
271 3 Ham. 383; 2 Caines, 179.
     3. Sometimes the writ of certiorari is used as auxiliary process, in
order to obtain a full return to some other process. When, for example, the
record of an inferior court is brought before a superior court by appeal,
writ of error, or other lawful mode, and there is a manifest defect, or a
suggestion of diminution, a certiorari is awarded requiring a perfect
transcript and all papers. 3 Dall. R. 413; 3 John. R. 23; 7 Cranch, R. 288;
2 South. R. 270, 551; 1 Blackf. R. 32; 9 Wheat. R. 526; 7 Halst. R. 85; 3
Dev. R. 117; 1 Dev. & Bat. 382; 11 Mass. 414; 2 Munf. R. 229; 2 Cowen, R.
38. Vide Bouv. Inst. Index, h.t.