A non-domiciled person (sometimes called a “non-dom”) is a person living in the UK but who considers their permanent home to not be in the UK.
Non-domiciled people can benefit from certain tax advantages, like not paying UK taxes on earnings from abroad unless they transfer that money into a UK bank account (for example, rental properties overseas). This is called “using the remittance basis” of taxation.
However, they also have to pay a special charge to maintain their non-dom tax status. Non-doms also lose the UK tax-free allowances like the Personal Allowance or the Capital Gains Tax Allowance.