A DPF (Diesel Particulate Filter) is a component in a diesel car's exhaust system that traps soot particles before they leave the exhaust, as part of meeting modern emissions rules.
What it means in practice: a DPF is designed to "regenerate", burning off the trapped soot automatically, during a sustained faster drive like a motorway run. Cars that mostly do short, low-speed journeys around town are the ones most likely to have DPF problems, since the filter never gets hot enough for long enough to clear itself.
A blocked or removed DPF is a genuine problem, not just an inconvenience: it can cause reduced power and trigger a warning light, and removing a DPF altogether affects the car's emissions, is typically an MOT failure, and is not legal for road use.