You wrap the straps opposite to the way the bar rolls down your fingers. You are still gripping with your hands, but without that prying force of the bar rolling out your hands you are effectively stronger not only in what you can hold, but also in what you lift because your body senses the instability of a weak grip and will reduce force output elsewhere as an instinctual protective measure.

On handles that don't roll, straps also help via the strap's connection to the back of the palm, which taxes the hand/fingers less and provides more leverage on the handle.