The bonus is civ wide and is a "hard-coded" 50% bonus to all production. The "hard-coded" nature makes it somewhat unique in that it does not appear as part of the Military Production bonus that's listed under "Abilities" in the Stats & Graphs tab of your Civilization Manager.

This bonus is also unique in that it does not "stack" like all other sources of bonus. Most sources of bonus "stack" by being additive, that is if you have a 50% bonus from one thing and a 30% bonus from another you end up with a total bonus of 80%. The artifical slave center (ASC) stacks by multiplying *all* production even production from other bonus. For example in the case I mentioned above if your "normal" military production was X then your total MP with an additive 50% and 30% bonus would be 1.8X, howver in the case of the 50% ASC bonus and another unrelated 30% MP bonus it would be 1.3X * 1.5 = 1.95X. In effect the ASC not only gives your normal production a bonus it also increases all other source of bonus as well.

The ASC is extermely powerful, the only downside is that there is no advantage to having more than one in the case you capture another civ's ASC.