Non-dom was a special tax regime whereby for 15 years they didnt look at your income from abroad provided it stayed abroad. It costs 30k from year 7 to stay in this regime.

This was great for people who just want to come to the UK to work say in finance for a few years but don't want to move their inheritance regime or finances from other countries. It was much fairer than most people make it out to be since most other countries dropped the double taxation agreement if you opted for this, therefore you would also pay tax in your origin country.