All you need is some paper, tape and a pair of scissors.
First, cut out a long, thin strip of paper.
Holding it the tall way, label the top left corner "A," the top right corner "B," the bottom left corner "C," and the bottom right corner "D."
Give the strip a twist and tape the two ends together so that "A" touches "D" and "B" touches "C."
Now check this out. If you start drawing a line around the strip, you'll end up right back where you started.
See it doesn't have a front or a back! The top and the bottom are the same. The twist in the strip connects what was the top to the bottom, making one big side.
What's really interesting about this strip is all the things you can do with it. Start cutting your strip down the middle, like you are cutting two, thinner strips. But you don't get two! You end up with a much larger, thinner Mobius Strip.