The Constitution of India provides for a parliamentary form of government, both at the Centre and in the States. Articles 74 and 75 deal with the parliamentary system at the Centre and Articles 163 and 164 in the states. The parliamentary government is known as cabinet government or responsible government or Westminster government.
The Prime Minister plays the leadership role in the parliamentary form of government. He/she is the leader of the council of ministers, leader of the Parliament, and leader of the party in power. The head of government (Prime Minister) is appointed by the head of state (President).
To read more about the Difference between Presidential and Parliamentary Forms of Government, check the linked article.