The meaning of for any service rendered by him outside India under section 80RRA 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 for any service rendered by him outside India.
Meaning of for any service rendered by him outside India defined by court
The phrase ‘For any service rendered by him outside India’ used in section 80RRA of the Income Tax Act came up before hon’ble Delhi High Court in K.R. Pradeep Vs. CBDT  155 TAXMAN 207/282 ITR 526/203 CTR 147 (DELHI) and it explained.
Meaning: The words ‘for any service rendered by him outside india’ in section 80rra would not include service rendered by a person who remains physically in india but the service is for some work which is done outside india.
Section 80RRA of Income Tax Act
Deduction in respect of remuneration received for services rendered outside India.
80RRA. (1) Where the gross total income of an individual who is a citizen of India includes any remuneration received by him in foreign currency from any employer (being a foreign employer or an Indian concern) for any service rendered by him outside India, there shall, in accordance with and subject to the provisions of this section, be allowed, in computing the total income of the individual, a deduction from such remuneration of an amount equal to—
(i) sixty per cent of such remuneration for an assessment year beginning on the 1st day of April, 2001;
(ii) forty-five per cent of such remuneration for an assessment year beginning on the 1st day of April, 2002;
(iii) thirty per cent of such remuneration for an assessment year beginning on the 1st day of April, 2003;
(iv) fifteen per cent of such remuneration for an assessment year beginning on the 1st day of April, 2004,
as is brought into India by, or on behalf of, the assessee in convertible foreign exchange within a period of six months from the end of the previous year or within such further period as the competent authority may allow in this behalf and no deduction shall be allowed in respect of the assessment year beginning on the 1st day of April, 2005 and any subsequent assessment year :
Provided that no deduction under this sub-section shall be allowed unless the assessee furnishes a certificate, in the prescribed form78, along with the return of income, certifying that the deduction has been correctly claimed in accordance with the provisions of this section.
(2) The deduction under this section shall be allowed—
(i) in the case of an individual who is or was, immediately before undertaking such service, in the employment of the Central Government or any State Government, only if such service is sponsored by the Central Government;
(ii) in the case of any other individual, only if he is a technician and the terms and conditions of his service outside India are approved in this behalf by the Central Government or the prescribed authority.
Explanation.—For the purposes of this section,—
(a) “foreign currency” shall have the meaning assigned to it in the Foreign Exchange Management Act, 1999 (42 of 1999);
(b) “foreign employer” means,—
(i) the Government of a foreign State; or
(ii) a foreign enterprise; or
(iii) any association or body established outside India;
(c) “technician” means a person having specialised knowledge and experience in—
(i) constructional or manufacturing operations or mining or the generation or distribution of electricity or any other form of power; or
(ii) agriculture, animal husbandry, dairy farming, deep sea fishing or ship building; or
(iii) public administration or industrial or business management; or
(iv) accountancy; or
(v) any field of natural or applied science (including medical science) or social science; or
(vi) any other field which the Board may prescribe79 in this behalf,
who is employed in a capacity in which such specialised knowledge and experience are actually utilised;
(d) “competent authority” means the Reserve Bank of India or such other authority as is authorised under any law for the time being in force for regulating payments and dealings in foreign exchange.
Updated up to Finance Act 2021.