It's not for oligarchs, but rather a clever feature that gives you an option to decide if you want to make the UK your permanent home and acquire the domicile.
Long story short - before entering the country with purpose of staying (work/investors visa, etc) you can declare your existing assets as "clean capital" and freely remit it to the UK without any tax implications. You can also do it later, but be aware of keeping the income on these assets separated from the clean capital.
After you entered the country you have like 15 years to benefit from non-dom and every year you may︀ at your convenience claim "remittance basis" for your tax report. If you don't claim it︁ - you pay regular taxes on all your income (both UK and offshore). If you︂ do - you only pay taxes on your UK income, but lose some basic tax︃ allowances (which is OK as long as your non-UK income is substantial).
First 7 years︄ it's "free" (you only lose your tax allowances), then it goes to 30k and more.︅ Still makes sense if you are making hundreds of thousands.
As long as you play︆ nice, don't control any foreign companies, it's a brilliant way to have a low tax︇ life in one of the best places in the world (business wise at least).