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.
Lord Asriel uses the example of tossing a coin to illustrate clearly to Lyra how every possibility is manifest in the multitude of parallel worlds. However it also has links to probability theory. Probability is a way of expressing the likelihood that an event will occur. This page explains the maths behind it a little more clearly.
The Sphinx is a legendary creature of Greek and Egyptian mythology, typically described as having the body of a lion and the head of a human being.
In Egyptian mythology, the Sphinx is portrayed as a male, whereas the Greek Sphinx has the face and breasts of a woman and often the wings of a great bird of prey. Another difference is that the Egyptian Sphinx is considered largely benevolent, as opposed to the more malicious Greek Sphinx.