Loop
The kaiju invasions cause the world to be reset every 16 years. As a result, the students grow up and die before reaching adulthood, and are then born again to repeat the cycle. This cycle is what they call a loop.
Once the kaiju gain control of every mainframe in all sectors, the world is automatically recreated as a new loop begins.
If you save your own data (or shift yourself) to Sector 0, then you will be able to skip the reset and end up in the new world, which is 16 years in the past, while maintaining your current appearance. However, you would no longer be human in the new loop, but merely a simulated personality that Universal Control has reconstructed.
"One loop ago" refers to one loop before the current time, and "two loops ago" refers to two loops before the current time.
The nurturing of the 15 members started once the terraforming of the new planet was completed, but the details of the terraforming's official "end date" are unknown. Therefore, the details on when the current loop began, or how many have passed before it, are unknown. However, based on the stability of the facility, it's believed that there have been at least 300 loops leading up to this point.