Third party insurance is the minimum legal level of motor cover in the UK. It pays for injury to other people and damage to their property caused by the policyholder, but never for damage to the policyholder's own vehicle.
In one line: Third party insurance is the legal minimum motor cover, paying others but not the driver's own car.
How third party insurance works
The Road Traffic Act 1988 requires every driver using a vehicle on a public road to hold at least third party cover for injury and damage caused to others. It does not pay to repair or replace the policyholder's own car.
If a driver causes a collision damaging another vehicle worth 6,000 GBP, third party insurance covers that claim in full, but the driver pays for their own repairs out of pocket, even if those cost more.
Third party, fire and theft adds protection against the policyholder's car being stolen or burnt, sitting between basic third party and comprehensive cover.
Third party vs comprehensive insurance
Third party insurance covers harm to others only, while comprehensive insurance also pays for damage to the policyholder's own vehicle, including in fault accidents.
Comprehensive cover is often cheaper than third party for some drivers, because the people who buy basic cover can present a higher claims risk to insurers.
Primary source: Road Traffic Act 1988 (legislation.gov.uk)