An NGO is a non-government organization with a charitable objective, for the betterment of the society in general. It can be started as a Trust, a Society, or a Non-Profit Company [Section 8 Company], depending on the activity you wish to undertake.
In India, NGO is an umbrella term for all non-profit organizations including Trust, Society, and Section 8 Company. Other names for such not-for-profit organizations are "Sangathan", "Sangh", "Sangam". Income tax exemption is available for all non-profit NGOs.
These are sometimes confused with non-profitable companies, which refers to a regular business is not making a profit.