Offshore is an accounting way of saying “abroad” or “overseas”.
If you’re a UK tax resident, you need to declare your offshore gains and income to HMRC, file a Self Assessment tax return and pay tax on them.
The only exception is if you declare yourself to be a “non-domiciled” person – but then you also lose your UK tax-free allowances and have to pay a special charge (it starts at £30,000 per year).
Another special situation is when you’re a UK tax resident and run a limited company that’s based abroad, and you’re its only director and shareholder. The HMRC will likely consider your company a UK tax resident and ask you to pay UK corporation tax for its profits (instead of the local corporation tax wherever your offshore company is registered).