Third party insurance is a legal requirement as per the Motor vehicles act 1988. You can run a vehicle without the OD component of the car insurance but you can not run a vehicle without the Third Party (TP) component.
Other than the legal cause, third party insurance comes in handy when the insured vehicle hits other vehicle, property or person. It covers the insured vehicle in case any liability claim arises for causing bodily injury, property damage, or death of the third party.