Presently there are three types of sectors in India - Government, Private and Civil Society Organisations.
The third one is commonly known as Civil Society or Civil Organisation as you have referred in your query.
Civil Organisation is basically the nomenclature for all the existing non government non profit organisations (NGOs) which are active in various areas in India.
These organisations are neither government type nor like private. They are basically to serve the society in various fields and are optionally funded by government, private enterprises and rich and capable Individuals.
These organisations (NGOs) do not work for profit making. There objective is -
1. To keep a watch on human rights violaton and bring to notice of Govt and fight for justice.
2. To bring the issues of poor and weaker sections in the notice of media and Govt.
3. Arrange and manage agitations and processions in favor of issues related to development of society.
4. To educate the public for their rights, facilities from Govt and citizens responsibilities and work like a communication conduit between the public and Govt.
5. To serve people in those areas where Govt machinery is not able to function either due to it's own inefficiencies or due to remote and inaccessible areas.
6. To generate, create, obtain and collect public opinion and put it to Govt for consideration and change of policies if required in the benefit of citizens.
The formation of a civil organisation requires registration in the office of Registrar in the same way as is done for companies. Certain procedure is to be followed and names of its members and other relevant information like objective, source of funds, address etc is to be provided.
Govt can close down those civil organisations (NGOs ) which are not complying with the guidelines and policies laid down by Govt for them. Some of the civil organisations are funded by foreign entities and these civil organisations should follow the foreign exchange regulations also. Recently there was a crackdown by Govt on some foreign funded NGOs and it was found that there are some discrepancies and violations and Govt has taken a stern view and some of these organisation were penalised.
Knowledge is power.