I have CIVanilla. I am on a mac, so our versions might be slightly different (or incompatible). Only PCs can host pitboss games. They are a persistent world with a clock. If you set it for 12 hours, everyone must take their turn before the 12 hours are up or it automatically goes to the next turn.
There are some other threads about setting it up, but one mentions that CIVanilla has problems w pitboss? Or it doesn't work or something? mb a patch needed.