DPF's are fitted to most modern diesels, and reduce the amount of particulates emitted by trapping them in a filter. When the filter gets full the engine will start what is called a regenerative cycle that burns off the excess soot in the filter. This will normally happen without the driver being aware it's going on.
However for the regeneration cycle to work the engine must be hot and running at higher revs, typically over 2,000 RPM for a period whilst the cycle takes place. The problems start with vehicles used on short journeys or around town, where the vehicle might not complete the regenerative cycle before reaching it's destination and being turned off.
If this happens a warning light will come on, and in some vehicles a warning sound will go off. It is VITAL that the driver immediately takes the vehicle on a run until the warning light is extinguished. Failure to do so will almost certainly damage the DPF beyond repair, and it will have to be replaced at a cost of several hundreds of pounds and this will NOT be covered by the manufacturer's warranty.
In extreme cases if the situation is not resolved where the DPF repeatedly tries to regenerate it will inject additional fuel into the engine, which can result in contamination of the engine oil which could result in serious engine damage.
If you know the use of a vehicle is going to make this process a real problem, then it would be best to select either a petrol or hybrid car instead of a diesel.