DataTable Columns can be reordered using drag drop by setting the reorderableColumns to true. onColReorder is a callback that is invoked when a column is reordered.
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export class DataTableColReorderDemo implements OnInit {

    cars: Car[];

    constructor(private carService: CarService) { }

    ngOnInit() {
        this.carService.getCarsSmall().then(cars => this.cars = cars);
    }
}

View on GitHub

<p-dataTable [value]="cars" reorderableColumns="true">
    <p-column field="vin" header="Vin"></p-column>
    <p-column field="year" header="Year"></p-column>
    <p-column field="brand" header="Brand"></p-column>
    <p-column field="color" header="Color"></p-column>
</p-dataTable>