A Bailiwick reduces the maintenance costs of all industrial buildings on the island it's built on by 10%. Be aware that this cost reduction doesn't affect trade, civil, military, governmental or irrigation buildings. It also allows access to statistical information on your settlement as well as acting as a place to write useful notes. Building multiple Bailiwicks on the same island does not grant any additional bonuses.
A Bailiwick's main function of reducing maintenance costs is not to be ignored. On any island with over 400 maintenance in industrial buildings, it will save you money (400*0.10=40; 40 being the maintenance cost the bailiwick itself).
Likewise, the Bailiwick's "Reeve's Book" ability to open a screen that displays all the different buildings you have on an island is indispensable for managing complex settlements efficiently. Regularly checking to make sure the appropriate number of buildings are being built to match production chains is the best way to optimize your gold balance.
When playing online with co-op players, the Bailiwick will notify the other team members when someone makes a note.