The President can declare three types of emergencies: national state and financial.
The President of India, after receiving a written communication of the decision of the Union Cabinet; may issue a proclamation of national emergency when the security of the nation, or any part thereof is threatened, or is likely to be threatened by war or foreign attack, or armed rebellion.
Every such proclamation is required to be laid before each House of Parliament. Such an emergency was declared in India in 1962 (Indo-China war), 1971 (Indo-Pakistan war), and 1975 to 1977 (declared by Indira Gandhi). In such an emergency, fundamental rights of Indian citizens can be suspended.
State emergency can be pro-claimed if the President of India is satisfied with the report of a Governor or otherwise, or on his own initiative that a situation has arisen in which that State Government cannot be carried on in accordance with the provisions of the Constitution.
President can announce financial emergency too. Such an emergency must be approved by the Parliament. It has never been declared.