The arising basis is the default way UK residents are taxed on their income and capital gains. Under this system, you pay UK tax on income and gains as soon as they’re earned, regardless of where in the world they arise. So, whether you receive rental income from a flat in France or dividends from shares in New York, HMRC expects you to report it in the UK tax year it’s received.
The alternative is the remittance basis, available to some people with foreign income, but unless you specifically claim it, you’ll be taxed on the arising basis by default.