The water in your central heating system flows from your boiler, where it is heated up, around all your radiators and then back to the boiler to be reheated and circulate again. A magnetic boiler filter is a small device that is installed into the pipework close to where the water goes back into your boiler.
As the water passes through the filter, a strong magnet attracts any fragments of rust and other magnetic debris (called magnetite or iron oxide 'sludge') and stops it from entering the boiler and causing damage or blockages. You will need to get the filter cleaned at the same time as your annual service to remove all the debris that has accumulated in it.
As well as the potential to damage your boiler, sludge in the radiators will cause cold patches at the bottom, so your heating will have to work harder to reach your set temperature, in turn increasing your fuel bill. Read more about why it is important to look after the water in your heating system.