The photo on the left is a knitted moebius. On the right is a paper model where you take a length of paper , draw a line along it, twist it around so the two edges are now opposite to each other and tape them together.
Now you can knit a moebius (google to find out how) but you can also simply knit a length, twist it as you did the paper, and stitch the ends together.
Now, I must admit the purple moebius is one I made using the right photo method as are the two below.