It affects construction time. When you open the city details screen you can see the current ratio there. Normally cities would have 1.0 so buildings would take 100% of the base turns to complete. With an administrator it would go down to 0.9 so only 90% of the turns would be needed. With a couple of administrators, the kindgom buildings that reduce construction time and the enchanted hammer spell you can easily reduce construction time to 0.1. That's when I first noticed there is a cap of 50 tiles per city. So I just moved all my administrators, recast the spell on my next biggest city... 
