Sub-hyperspace was the name given by members of the First Order to a hole in the space-time continuum through which phantom energy traveled. Unlike typical hyperspace, which moved across the galaxy, sub-hyperspace would move through the galaxy. The First Order's Starkiller Base was able to collect a form of dark energy called quintessence, transform it into phantom energy, and unleash it along a linear path through sub-hyperspace, enabling it to destroy entire star systems across vast interstellar distances in real-time.
According to a tweet from Pablo Hidalgo, the vast quantities of energy released by firing of the Starkiller weapon had the ability to create a temporary rip in sub-hyperspace, thus allowing the Hosnian system's destruction to be viewed from across the galaxy as it occurred.