DataTable - Responsive DataTable columns are displayed as stacked in responsive mode if the screen size becomes smaller than a certain breakpoint value. This feature is enabled by setting responsive to true.
Responsive

export class DataTableResponsiveDemo implements OnInit {

    cars: Car[];

    constructor(private carService: CarService) { }

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


<p-dataTable [value]="cars" [rows]="10" [paginator]="true" [pageLinks]="3" [responsive]="true">
    <header>Responsive</header>
    <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>