Negative punishment means removing something the dog wants immediately after a behaviour, which makes that behaviour less likely to happen again. "Negative" refers to something being taken away, not to the method being harsh, and in practice this tends to be one of the gentler, more widely used tools in modern training.
A common example is ending a play session the moment a dog's teeth touch skin during rough play. The dog loses something they were enjoying, and over repeated instances, the biting during play reduces.