Diesel engines tend to be larger/bigger/heavier than petrol engines due to higher compression/pressure inside. They warm slower. Cold engine needs a rich mixture and that causes polution with unburnt fuel (mostly carbon). These devices are designed to filter that.

The downside is that engines used for short trips at low power (city driving) rarely get to high enough temperature to burn the carbon in the filters. Filters/catalytic converters get clogged and cause engine warnings / errors and bad performance.