Third party car insurance is normally the cheapest of the insurance policy levels. It covers any third party (not you or your car) in the event of an accident. It also protects any passengers you might be carrying at the time of an accident.
Lets take a look at an example of how this would work. We have two drivers and two cars, Person A + Car A and Person B + Car B.
Person A has his/her car insured with third party cover, person B's insurance cover is irrelevant. Person A pulls out in front of Person B and causes an accident and as a result Person A admits he/she was at fault.
In this situation Person A's insurance company would pay to repair or replace Person B's cars, they would also pay for any injuries or treatment to Person B if the need arose.
However, as Person A is only covered third party, their car will be not covered and therefore the insurance company will not pay for any repairs or damage to car A.
Also, as the policy only offers thid party protection, your insurer will not pay out in the even of a fire or theft of your car.

Third party insurance is recommended if the cars value is approximately £1000 or less. Third party cover is popular with new drivers with low valued cars.