The Administration Center improvement provides one extra administrator and provides an influence adjacency bonus. It becomes available with the Galactic Governance tech. I had been under the impression that it was a one per planet improvement but looking at it now I don't see that in the XML.
If you're interested, there's also my Administrator Training Institute mod, available from Nexus (nexusmods.com) that considerably predates the addition of the Administration Center to the game, and provides the same +1 administrator but has additional adjacency bonuses. Even though it's old it still works with the Crusade, Intrigue, and Retribution DLCs.