The Preamble to the Constitution of India declares India as "Sovereign, Socialist, Secular, Democratic, Republic". Sovereignty implies that India is free and has the authority to conduct its own affairs and governance. Democratic in the sense that the supreme power is possessed by people of the country. India has a Parliamentary Democracy. Republic means power is given to people or representative they elect. India has an elected head called the President who is elected indirectly.
Political sovereignty means residing of ultimate power in the hands of people who elect their representative sovereign.