Take a long, thin strip of paper... 4 cm by 24 cm, for example. Anything reasonably close
will do. Give one end a half twist and then tape it together. It should look
similar to this:
(except it doesn't have to be blue.)
What you now have is a one-sided, one-edged piece of paper called the Mobius strip. To see
that it has only one side, try drawing a line along one side and continue until you end up
where you started. Like this:
Now see if you can find the "other side"... the side without a line on
it. You won't find the other side, because there isn't one!
To see that there is only one edge, use a different colored pencil or pen and draw a line
along the edge on one side of the center line you drew.
Eventually you will end up where you started, and you will see
that there are lines along "both" edges of the Mobius strip.
But since you drew only one continuous line, there must be only one edge!