What is FATCA?
FATCA is Foreign Account Tax Compliance Act, a law enacted by USA in 2010. According to this law, any individual who is resident of USA (citizens or green card holders) or financially connected to the US or have any tax residency in US have to declare all their foreign income and investment details to US Tax Authorities. The law was enacted to prevent tax evasion through offshore investments by US residents.
India is signatory of the above law and hence all the financial entities like Banks, Insurance Companies, Mutual Funds, Brokerages, etc have to furnish their client information to the Indian Government, which in turn would share it with US Government. In case you have no income connection with USA, you are not impacted but still need to give the declaration.