This privelege allows so-called "non-doms" to avoid paying tax on in the UK on income kept abroad. This privelege is granted on very tenuous and often fabricated claims to be "domiciled" in other countries.
Why does this idea matter?
Everyone in this country should be subjected to the same tax regulations. This bizarre law effectively turns the UK into a tax haven for non-domiciled resdients. It might also explain why 80% of hedge funds in the EU are based here. Take Zac Goldsmith – he was born and lived all his life in the UK but until recently took advantage of this status because his father had French citizenship, though you could never tell by his accent!