Simply explained: Through a series of financial trades, multiple players get reimbursed for a tax that was never paid or only paid once. While those involved -- banks, companies, or individuals -- make a profit, society loses billions of taxpayer euros.
You can think of it like a scam for child benefits. Imagine a German couple has no children, but their friend from London is visiting with their kid. Although the child does not really live with them, the couple registers the friend’s child with the authorities as their own. When the British friend visits another acquaintance, that person also registers the child as their own. They go on to visit three, maybe four more friends in Germany -- each of whom registers the child as their own.
When the British friend and their child return to the UK, the child is registered once again with its actual parent. But the German government does not know this, and pays child benefits to each of the German families who participated in the scheme. The stolen child benefits are then split among all the families taking part in the scam.
In the case of cum-ex fraud, stock shares are strategically traded between multiple entities so that on paper, it seems like they are all owners. And instead of child benefits, millions of taxpayer euros are paid fraudulently to each party claiming reimbursements.
The bankers take advantage of the fact that tax offices did not detect the fraud. But in the end, the money they scam is missing from other places. For the renovation of a kindergarten, for example.