Parallel incarnations refers to the phenomenon in which all your past lives are actually occurring now. But just to organize it in a way that makes sense to the brain, we say they were in the past. This is how the Twin Flame phenomenon works too—but with regard to space. Your soul is in two places at the same time.
Einstein showed, through his Theory of Relativity, that time is an illusion. Time is a convenience created by humans so we can communicate with each other and organize physical reality. But in metaphysics, all things are simultaneous. All of our lifetimes are occurring now. We are just putting them into sequence to get a grasp on them and derive meaning.
It’s like going into an imaginary giant multiplex cinema where thousands of movies are all playing at once. And you want to see as many movies as you can. All the movies are there and it your choice which one you want to start with and which one you want to see next. But they all will be playing forever.
Your lifetimes are that way. You have past and present and future lifetimes all in the same space as you. The illusion is that they are in different times. And so it goes with parallel lifetimes, or twin souls, which are in the same time, but in a different space. In some cases you can even be a soul triplet.
Parallel incarnations show us that time is an illusion. All lifetimes are simultaneous -- past, present, future, parallel, overlapping. All of them are happening at once.