The Seaport is one of the most complete boosters in the entire game! It is worth the time invested to build it ASAP in every Harbor you have, because it will provide significant bonuses to its parent city.
Maybe the most important feature of the building is the boost to Fleet and Armada training speed, which is similar as the Military Academy's boost for land-based formations. Thanks to it, a weak civilization may be able to churn out a much stronger fleet much faster than its enemies will expect, and a strong nation will build an even stronger fleet, again that much faster.
Another great boost, as per the Spring 2017 Update, is the Gold yield added to all coastal tiles. If you have lots of these and are able to work them, you could potentially turn this city into a veritable Gold mine! Thanks to this boost, and a similar new bonus for the Lighthouse, it is now worth it to have Coastal cities covering lots of water.
Historical Context Edit
The sites of ancient ports were selected to optimize access to land or river routes, protect the anchored shipping, and maximize harbor fees – Guangzhou in Qin China, Piraeus for Athens, Canopus and Alexandria in Egypt, Lothal for the Harappan, Rome's Ostia Antica. More than just a harbor, a seaport offered all the necessities for sea-going vessels and their crews: cordage and carpentry workshops, docks and slips, bars and brothels, warehouses, and so on. The seaports of Europe were the launching points for the exploration and colonization of the world, as well as the naval bases that figure prominently in military history. Commercial empires rose and fell tied to the fate of their seaports: Phoenicia, Srivijaya, Portugal and others. Although less common than those facing the seas, inland ports such as New Orleans or Calcutta gave vast regions access to the oceans. Today the great ports of the world – Port Said, Hamburg, Shanghai, Melbourne, Santos, Hong Kong, Los Angeles and Vancouver, to name a few – are a forest of cranes, a maze of roads and rail, a city of warehouses and storage tanks, all devoted to making a profit from export and import.