AO Rebirth can operate an Anarchy Online compatible server, but describing the project only as a "private server" leaves out most of what is being built. Behind a functioning character standing ingame are multiple independent services and systems responsible for different parts of the game, such as:

Account authentication and login
Character creation, selectionand persistence
Playfield loading, populating, zoning
NPC spawning, movement and patrol behavior
Combat, aggro and retaliation
Character statistics, skills and abilities
Inventory management, equipment
Items/nanos, shops and vendors
Credits, experience and progression
Missions, quest progression, rewards
Doors and interactive objects
Chat, teams, organization, looking-for-team
Player state, pets
Loot, death and resurrection
Insurance-related behavior
Database persistence
Network protocol handling
And those are only the systems visible from the player's perspective. There is also an extensive engineering layer required to build, test, validate, deploy, monitor, and maintain the server itself.