The meaning of high court under sections 256 to 260 of the Income Tax Act is not defined in the act itself. But we can take guidance from decisions by various high courts. Here is an excerpt of the court’s order in which the Hon’ble High Court tried to explain the meaning of high court.
Meaning of high court defined by court
The phrase “high court” used in section 256 to 260 of the Income Tax Act came up before hon’ble Andhra pradesh high court in IT Vs. Parke Devis (India) Ltd.  106 Taxman 16/239 ITR 820(AP) and it explained
Meaning : The words ‘the high court’ occurring in section 256 have obvious reference to the high court within whose jurisdiction the tribunal is located.
Section 256 of Income tax act
Statement of case to the High Court.
256.(1) The assessee or the Principal Commissioner or Commissioner may, within sixty days of the date upon which he is served with notice of an order passed before the 1st day of October, 1998, under section 254, by application in the prescribed form, accompanied where the application is made by the assessee by a fee of two hundred rupees, require the Appellate Tribunal to refer to the High Court any question of law arising out of such order and, subject to the other provisions contained in this section, the Appellate Tribunal shall, within one hundred and twenty days of the receipt of such application, draw up a statement of the case and refer it to the High Court :
Provided that the Appellate Tribunal may, if it is satisfied that the applicant was prevented by sufficient cause from presenting the application within the period hereinbefore specified, allow it to be presented within a further period not exceeding thirty days.
(2) If, on an application made under sub-section (1), the Appellate Tribunal refuses to state the case on the ground that no question of law arises, the assessee or the Principal Commissioner or Commissioner, as the case may be, may, within six months from the date on which he is served with notice of such refusal, apply to the High Court, and the High Court may, if it is not satisfied with the correctness of the decision of the Appellate Tribunal, require the Appellate Tribunal to state the case and to refer it, and on receipt of any such requisition, the Appellate Tribunal shall state the case and refer it accordingly.
(2A) The High Court may admit an application after the expiry of the period of six months referred to in sub-section (2), if it is satisfied that there was sufficient cause for not filing the same within that period.
(3) Where in the exercise of its powers under sub-section (2), the Appellate Tribunal refuses to state a case which it has been required by the assessee to state, the assessee may, within thirty days from the date on which he receives notice of such refusal, withdraw his application, and, if he does so, the fee paid shall be refunded.
Section 260 of Income tax act
Decision of High Court or Supreme Court on the case stated.
260.(1) The High Court or the Supreme Court upon hearing any such case shall decide the questions of law raised therein, and shall deliver its judgment thereon containing the grounds on which such decision is founded, and a copy of the judgment shall be sent under the seal of the Court and the signature of the Registrar to the Appellate Tribunal which shall pass such orders as are necessary to dispose of the case conformably to such judgment.
(1A) Where the High Court delivers a judgment in an appeal filed before it under section 260A, effect shall be given to the order passed on the appeal by the Assessing Officer on the basis of a certified copy of the judgment.
(2) The costs of any reference to the High Court or the Supreme Court which shall not include the fee for making the reference shall be in the discretion of the Court.
Updated up to Finance Act 2021.