This neat little object has only one side to it. What might appear to be a second side is actually just an extension of the first side. To prove this to yourself, draw a line down the middle of the loop; it should eventually meet itself after following both sides of the loop.
The Möbius strip is named after August Ferdinand Möbius, a German mathematician of the nineteenth century. He was a pioneer in topology, being the first to discover one-sided surfaces, including the Möbius strip.
(Just for curiosity's sake, heres a little picture of the impossible triangle, which is also somewhat related to all this stuff...)
This interesting mathematical phenomenon has also been extended into literature by authors such as Julio Cortazar and Jorge Borges. For example, Cortazar's story, "Continuity of Parks", is about a man reading a novel in which another character murders the man reading the novel. This story wraps from end to beginning without interruption, and the novel within it would have an infinite number of novels within themselves, all of which are the same novel. Sort of like looking into a mirror which is standing opposite of another mirror.
Now back to Möbius strips... The painting along the side of the page was created by none other than the spatial genius; M. C. Escher, a famous composer of interesting topographical depictions. This piece shows a Möbius strip with ants crawling on and around it.