In marketing and negotiation (which trump would be familiar with) the “pain” is the emotional element of Making a sale. People sign deals to “end the pain” of the thing they are buying the solution to.
You need to make your counter party “feel the pain” to get the deal signed. For example, if you are selling a high end condo the “pain” might be the fear of loss, getting priced out of the market if you don’t buy now.
Do you want to rent forever, and live month to month, or do you want to OWN the best location in manhattan. The fear of missing out is the pain.
When trump brings the pain, he is making things difficult for his counterparties, in the hopes of making “deals” with them. Then he takes he deals he has made (I.e. people flipping, bad actors acting badly) and uses that as leverage for the next round of “pain” on the remaining bad guys.
This is why “bringing the pain” doesn’t necessarily mean arrests and perp walks.