Hyperspace travel is a means of achieving faster-than-light travel through folding space and moving between two points along that fold. Hyperspace travel was slowly achieved through the Nguyen-Nguyen Principle, which discovered a means to identify a point in space through a relationship with another point and then fold space in order to travel between those points instantaneously.
"Hyperspace comes out of an area of physics called quantum theory. It postulates that what we think of as empty space is instead comprised of small particles. Within that is another theory that there are more dimensions than the ones we are capable of experiencing and that time and distance are not the immutable scientific facts we believe they are. Some theories express that other dimensions exist and that these other dimensions can be accessed to move more quickly between places on this dimension. "
From Five Steps Across the Abyss
Brandon Sheehan was the first person to travel in hyperspace in the Year 149 ac. His experimental trip (from one platform to another next to it) demonstrated the safety of hyperspace on the human psyche.