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. In case you'd like to control the stacked mode manually regardless of screen size, use the stacked property.
Responsive

export class DataTableResponsiveDemo implements OnInit {

    cars: Car[];
    
    stacked: boolean;

    constructor(private carService: CarService) { }

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


<button pButton type="button" (click)="toggle()" style="margin-bottom:10px" label="Toggle" icon="fa-list"></button>

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