“Non-dom” describes a UK resident whose permanent home – or domicile – for tax purposes is outside the UK.
It refers to a person’s tax status, and has nothing to do with their nationality, citizenship or resident status – although it can be affected by these factors.
A non-dom only pays UK tax on the money they earn in the UK. They do not have to pay tax to the UK government on money made elsewhere in the world (unless they pay that money into a UK bank account).
For wealthy individuals, this presents the opportunity for significant – and entirely legal – savings, if they state a lower-tax country as their domicile.