Firms can always shift their profits from one tax territory to another via various methods.
Consider a simplistic example, let’s say we have firm ABC that has most of its business in Sweden. The owners of ABC can set up another parent company, let’s say ABC global in some tax haven like Luxembourg. Afterwards they can transfer some intellectual property (or other difficult to value assets - typically some intangibles) to the ABC global.
Then when ABC Sweden manages to have to have let’s say 100,000€ profit, the Luxembourg based ABC global will decide to lease the intellectual property (eg logo) to ABC Sweden for 100,000€. This extra cost will cause ABC Sweden to have zero profit in Sweden while now ABC global in Luxembourg gets 100,000€ profit that now will be taxed there at the their very low corporate taxes.
The above is just an oversimplified example of course, the methods how this is done are always evolving as government regulators always play cat and mouse game with corporations. If you want to know more details you can have look at topics such as transfer pricing (see Alles,& Datar, 1998 or Hirshleifer, 1956).
Alternatively, and this what is directly referenced in that article, the parent company even can be located in the US, and just let it’s foreign daughter companies to reinvest profits they earn in each individual foreign market (eg use that profit to buy new building, invest in R&D etc, or to build a war chest). This still makes sense for the company, as A) doing so still makes company more valuable and thus increases shareholder value, B) if they build a war chest they can always bring that money home at some unspecified future if US decides to lower its taxes (like the Trump tax cuts).
Again the above is only very rough sketch of how this is done, the details always evolve following current tax regulations that are changing virtually every year in some small or bigger way around the world.
Can you explain how this works and why it is considered bad by some people on the left specifically?
This is not an economics question but moral question, so you would do better to ask this on philosophy stack exchange. This being said in short, answer whether the above is bad or ok depends on your moral framework. On a fundamental level this is not much different from ordinary people also trying to optimize their tax rates by taking advantage of various loopholes (eg people trying to claim as many deductions as possible or people avoiding VAT by having friend with a business buy them the product for them - since business get VAT rebates). So if you adopt some deontological (rules/action based) ethics, which says trying to minimize your tax rate (within legal bounds) is acceptable, then the (legal)corporate tax optimization should also not be a moral issue.
However, the ideology of modern (liberal) left is underlined by Rawlsian moral framework (or at least in literature that’s the basis for it, I doubt that most people on either left or right know any moral philosophers) which is governed by consequentialist Max-Min principle (although Rawls full framework has non-consequentialist elements so technically it is a hybrid moral framework for economics the Max-Min rule is the most relevant part). Under this ethical system actions are good if they help to maximize welfare for the poorest members of society. So under the Max-Min principle it’s consequences that matter not rules. Taking advantage of tax loopholes is fine if you are poor, but if you are rich corporation it is bad as resources from those taxes could be redistributed to the poor (assuming that the parameters of economy are such that this would still increase the welfare of poor eg we are not already at the point where taxes are so high that extra taxes cause so much distortions to the economy that it lowers welfare of poor more than they gain from extra redistribution).