Imagine your duvet cover, but sewn up at the bottom rather than buttons/poppers. Then it has a big circle cut in the middle of the top side.
So rather than having to feed your duvet all the way in from one end, you lay the cover on the bed, put the duvet on top and just push the corners in and give it a quick shake/smooth.
DF has them in lots of colours and will put two on opposite ways up so you have (say) a navy cover with a yellow circle in the middle, or a patterned circle and plain cover or vice versa. I think she tends to change the outer one and leave the inner one on for a couple of washes. I suppose you could just have the white of the duvet showing, but it might not look as nice.