Cryptophasia, the phenomenon of twins having their own language or is it a psychology myth? From the moment of conception twins are together, relying on each other in ways that are not noticeable to others. Twins understand each other in different ways and communicate in diverse ways leading people to believe that twins do have their own language.
As amazing as creating a new language is, from what I learned in my psychology book, languages have different morphemes and phonemes that make it unique. That would be pretty hard to conquer for young children to achieve that. They may understand it, but others do not.
Instead of twins creating a whole new language, I believe it comes down to the bond they have developed and how well they read one another. Being together for their whole life, an everlasting bond is something that cannot be broken. When you are with someone for that long, a new type of language is created, it is called body language. It is a language that is more discrete and different for many people. Body language is observing peoples movements to help understand them.
In the Youtube video, "talking twin babies" the two babies are repeatedly making the same noise, but watch their bodies. They use body movements with hands and feet to communicate. As a watcher of this video, translating their conversation is difficult next to impossible to understand, but to the twins they are having a lovely conversation next to the fridge.