The use of parallel universes is a popular and widely-used literary device in both written and visual fiction, but it does have a grounding in scientific theory.
In Lyra's world, it's mentioned that the "multiverse" theory was proposed by renegade theologians (physicists in Lyra's world) called Banard and Stokes. In reality, the term "multiverse" was coined by American philosopher William James in 1895. The structure of the multiverse varies depending on the nature of the hypothesis, as does the nature of the each universe within it and their relationship with each other. Cosmologist Max Tegmark provided a taxonomy of universes beyond our own, and in the video he explains them far more clearly than I could.