A nonâ€“domiciled resident is a person living in the UK, but with links to another country such that their residence of the UK is deemed temporary for tax purposes.
A fuller explanation is given by HM Revenue & Customs (HMRC):
4.1 Domicile is a general law concept. It is not possible to list all the factors that affect your domicile, but some of the main points are explained in this Chapter.
4.2 Broadly speaking, you are domiciled in the country where you have your permanent home. Domicile is distinct from nationality or residence. You can only have one domicile at any given time.
Domicile of origin
4.3 You normally acquire a domicile of origin from your father when you are born. It need not be the country in which you are born. For example, if you are born in France while your father is working there, but his permanent home is in the UK, your domicile of origin is in the UK.
Domicile of dependency
4.4 Until you have the legal capacity to change it – see paragraph 4.5 – your domicile will follow that of the person on whom you are legally dependent. If the domicile of that person changes, you automatically acquire the same domicile (a domicile of dependency), in place of your domicile of origin.
Domicile of choice
4.5 You have the legal capacity to acquire a new domicile (a domicile of choice) when you reach age 16. To do so, you must broadly leave your current country of domicile and settle in another country. You need to provide strong evidence that you intend to live there permanently or indefinitely. Living in another country for a long time, although an important factor, is not enough in itself to prove you have acquired a new domicile.
4.6 Before 1974, when you married you automatically acquired your husband’sdomicile. After marriage this domicile would change at the same time as your husband’s domicile changed. If your marriage ended, you kept your husband's domicile until such time as you legally acquired a new domicile.
This rule is modified by the terms of the double taxation agreement between the UK and the USA. A marriage before 1974 between a woman who is a US national and a man domiciled within the UK is deemed to have taken place on 1 January 1974 for the purpose of determining her domicile on or after 6 April 1976 for UK tax purposes.
4.7 From 1 January 1974 your domicile is not necessarily the same as your husband's domicile. It is decided by the same factors as for any other individual who is able to have an independent domicile. If, however, you were married before 1974 and had acquired your husband's domicile (see paragraph 4.6), you retain this after 1 January 1974 until such time as you legally acquire a new domicile.
4.8 From 6 April 1996 registering and voting as an overseas elector is not normally taken into account as one of the factors for determining whether you are domiciled in the UK, for the purpose of establishing your tax liability here.
Tax treatment of those not domiciled in the UK
4.9 Those who are resident in the UK but not domiciled here receive special tax treatment in respect of income and gains arising outside the UK. For details, see paragraphs 5.12 and 6.2 (income tax) and 8.8 (capital gains tax). We will consider the question of your domicile only where this will affect your current tax liability.
For inheritance tax purposes, see booklet IHT 18 'Inheritance tax. Foreign aspects'.
HM Revenue & Customs (Internal Link)