This page explains the rationale of hyperspace in Naev, and how it is represented in the game.
Hyperspace is conceived as a set of rules unrelated to the rules in realspace. One of the properties of hyperspace is that it allows ships to enter it at one point in space and exit at a completely different point.
The exact method of travel in hyperspace is not made explicit, but there is a period of time during which the ship is not present anywhere in realspace (relativity is waived in Naev). This implies that the ship spends some time in hyperspace during the journey from one point to the other. However, pilots don't experience this time. The ship is experienced as making the transitions between points nearly instantly. It has also been thought that hyperspace would allow for more than travel, however nothing has been achieved. It is not known entirely what happens to an object when it enters.
The time it takes to jump depends on the mass of the object. Life support systems on modern ships also affect the entire process of hyperspace, however even though the best scientists have been trying to solve the issue it has not been accomplished.
Although a ship can enter hyperspace anywhere in realspace and travel to any other point in realspace from there, the energy costs involved in doing so are exorbitant, to the point that the generators aboard even the biggest ships can only sustain jumps a fraction of a solar system's radius.
To travel to another solar system, ships must make use of spatial anomalies that exist naturally in most solar systems. These anomalies represent a "thin membrane" in realspace that makes it easy for a ship to pass into hyperspace. The ship then enters what could be considered a "path of little resistance" in hyperspace that leads to a similar anomaly in another solar system. Nobody is certain whether or not it's possible to deviate from the path and end up in another location, but it has never been achieved.
The spatial anomalies in Naev are referred to as jump points. Jump points appear on the playing field as funnel wireframes. In order to jump to another system, ships must approach the corresponding jump point before the hyperdrive can be engaged. It is to note that the jump points are not actually visible to the human eye, the funnel wireframe is augmented reality displayed by the ship's systems.