In the Republic of India, the phrase "President's rule" refers to the imposition of Article 356 of the Constitution of India on a State whose constitutional machinery has failed. In the event that a State government is not able to function as per the Constitution, the State comes under the direct control of the central government; in other words, it is "under President's rule". Subsequently, executive authority is exercised through the centrally appointed Governor, who has the authority to appoint retired civil servants or other administrators to assist him.
On the other hand, when the State government is functioning normally, it is run by an elected Council of Ministers, who are collectively responsible to State's legislative assembly (Vidhan Sabha). The Council is headed by the Chief Minister who is the de facto chief executive of the State; the Governor is only a de jure constitutional head. However, during President's rule, the Council of Ministers stands dissolved, the office of Chief Minister becomes vacant and the Vidhan Sabha is either put in suspended animation or dissolved (necessitating a fresh election).
In the state of Jammu and Kashmir, failure of constitutional machinery results in Governor's rule, imposed by invoking Section 92 of the Constitution of Jammu and Kashmir. The proclamation is issued by the state's Governor after obtaining the consent of the President of India. If it is not possible to revoke Governor's rule before within six months of imposition, President's Rule under Article 356 of the Indian Constitution is imposed. There is little practical difference between the two provisions.
Following its landmark judgement in the 1994 Bommai case, the Supreme Court of India has clamped down on arbitrary impositions of President's rule by central governments. Chhattisgarh and Telangana are the only states where President's rule hasn't been imposed so far.