In the book Halo: Ghosts of Onyx, it is revealed that at the core of Onyx is a Slipspace rift that shunts those that pass through it to a structured Dyson Sphere, dubbed beforehand by the Forerunners as a Shield WorldInstallation. It is separated from a normal space-time symmetry by advanced Forerunner Slipspace technology. Although Dr. Halsey calls it the Micro Dyson Sphere, the Sphere is 300 million kilometers (or approximately two astronomical units [1 AU is 149,598,000 km]) in diameter on the inside. The Micro Dyson Sphere's star has a spectra and energy output slightly smaller than the dimensions of Sol. This was going to be the haven where the Forerunners were to seek refuge when Halo activated, but no one knows what went wrong with their alleged plan, as the expanse appeared to be completely deserted when UNSC forces arrived. In Halo 3, these circumstances were revealed to be the result of the betrayal of the Forerunner AI Mendicant Bias, whose defection to the Flood forced the Forerunners to abandon their plans to evacuate into the shield installations.
Basically, the structure fulfills its function as a "Shield World" perfectly. It protects the occupants of it and gives them a huge "world" to live in. Potentially, an entire new civilization could be constructed in a Dyson Sphere.
After their arrival in the Forerunner-constructed Dyson Sphere, Dr. Halsey explains the structure. She labels it a Micro Dyson Sphere because it is in fact very small, or perceived to be small when viewed from normal space. Linda also describes it as being in the bottom of a large bowl.
The Micro Dyson sphere is located in a factually compressed Slipstream space. In other terms, any object inside might appear to be a certain size, but inside the Slipstream bubble it is much, much larger. Consequently, they never left Onyx, but simply entered a Slipspace bubble.
In Halo Wars, another type of Micro Dyson Sphere appears. This Shield World is vastly different from the Onyx installation. Unlike Onyx, which was made of trillions of Sentinels over which a planetary surface had formed, this world was built in a method similar to a Halo Installation. It was a hollow structure with planetary surfaces on the interior and exterior being supported by numerous pillars. Inside this was a more familiar construct of ship-sized portals allowing access from an opening on the outside to the interior world. The interior was somewhat similar to Onyx's Dyson Sphere, possessing an artificial sun, though it and the entire structure are on a far smaller scale. However, unlike Onyx, it was seemingly not only designed as a bomb shelter, but also as some sort of harbor, shipyard, or hiding place for ships, as it contains The Apex, which had dozens of Forerunner ships stored within it