Maybe a little explanation is necessary…
With an 8 bit grayscale picture you ‘only’ have 256 values from black to white. This looks smooth enough as an image, but when you use that as height information, you will see the ‘steps’.
With 16 bit, you’ll have 65536 different values and although there is still stepping in the heights, you won’t see it any more.
Like when an image is pixelated, you increase the resolution so that it looks smooth.