The remittance basis can be used where an individual is UK resident, but is not domiciled. If that persion chooses not to remit income arising outside the UK, while they are UK resident, then it is not taxable in the UK.
If the income is remitted to the UK in a later tax year, it will be taxable in that tax year. The remittance basis rules change when someone has been resident in the UK for 7 or more of the preceeding 9 tax years. The individual will lose their personal allowance / annual exempt allowance and be taxed on a fixed sum of £30000.00, plus their UK income and gains. The rules then change if the individual has been resident in the UK for 12 or more of the preceeding tax years. The individual will lose their personal allowance / annual exempt allowance and be taxed on a fixed sum of £60000.00, plus their UK income / gains.
Finally, once a non domiciled person is resident in the UK for 16 years plus, they become 'deemed domiciled' and become subject to tax on their 'world-wide' income in the tax year that it arises. There are guidance noted on residence, domicile and remittance here.
Guidance note for residence, domicile and the remittance basis: RDR1