The ORION Project, sometimes referred to as Spartan I, was an Naval Special Warfare program, overseen by the Colonial Military Administration, tasked with producing special advanced warfare squads to combat the Insurrection.
However, expectations for the new soldiers were not met, and the project was deactivated in 2506, and all members reassigned to other Special Operations units.
The children of Spartan 1.0s are called Spartan 1.1s, including Janissary James and Kevin Morales. There are sixteen 1.1s. They have much of the same augmentations as their parents, though without the same military training. Some of them tried to create their own army to fight the Covenant, but just as they were about to bring the fight to the Covenant, the Covenant invaded Earth.
In the years following the deactivation of Project ORION in 2506, the effectiveness of small forces combating the insurrectionists became too large for the UNSC to manage. As the attacks were becoming more effective, and the military's responses heavier; the need was growing for more large-scale military campaigns.
By 2517 the Office of Naval Intelligence concluded that the instability of the outer colonies would continue to escalate and unless drastic military measures were taken, it would result in a massive war between the inner colonies and the outer colonies.
The SPARTAN-II project, was conceived by Dr. Catherine Halsey of ONI's Section 3, as the successor to the original ORION project and the best possible solution to end the conflict.
You can read more about the ORION project on Halopedia.