A möbius strip is when a single plane is twisted and connected to itself. To make it more simple, think of a strip of paper. you have two ends of the strip of paper. you can connect the two ends to make a loop. Or you can twist the paper and then connect the two ends. This is a möbius strip. Though it may not seems like much, but by connecting the two ends of the strip of paper with a single twist in it, you have created a single-sided paper. Try taking a marker and draw a line on the strip, following the curves of the paper. You will end up in the same place you started, because you have essentially created a one-sided object that is both fluid and infinite.
The first time it is actually confirmed by BlockBerryCreative that the möbius strip is part of the LOONAVERSE is on the dlrowehtanool website, while the members of yyxy were being introduced, along with the Eden DNA (more information in dlrowehtanool.)
A single gif of a möbius strip was available on the website, with the LOONA logo in the center of it. This gif immediately went viral, and many speculate that this means the Universe the loona members are in is the shape of a möbius strip.
This also created the idea that there is more to the LOONAVERSE than meets the eye. The möbius strip is also considered to be the most important part of the LOONAVERSE, as Kim Lip said in an interview with DAZED.
If you were to draw a picture of a möbius strip, you'd give it three sides. One side in the back, one in the front, and another where the twist occurs. These are the dimensions in the LOONAVERSE. But as you'd probably notice, it's still a piece of paper. And paper has two sides, which is why each dimension of the LOONAVERSE has two sides, a light and a dark side. And it's also important to mention that the dark side mirrors the light side, meaning everything is flipped. This entire concept can be pretty confusing, so we've linked some basic videos about the möbius strip, some LOONA-releated and some not. There have been theories that the universe LOONA lives in is actually in the shape of a möbius strip, but as debunked by twinfish, that is completely impossible. Instead the möbius strip applies to the three different dimensions of the LOONAVERSE, that being Earth (LOONA 1/3), The Cosmos (ODD EYE CIRCLE), and Eden (yyxy). This is more important in some parts of the LOONAVERSE than in others, for example it isn't mentioned at all in ViVi's music video, but is essential to Choerry's music video.