Shipyard is where you build and repair ships. They are only available in Hanseatic Towns and Offices, while trading stations only have Repair Docks (that cannot build ships).
Building and repair contracts will gradually improve a shipyard (and Repair Dock), allowing it to build better ships and to repair them faster. This will also enable the Weapon Smith to produce more advanced weapons.
Improved Shipyards
In the beginning of the game, the shipyards can build ships with lowest cargo capacity (for example, 
150 Snaikka). Later on they gain enough experience to start building Hulks, and the ships they build have higher capacity (for example, 250 Snaikka). Higher volume of activity will speed up the improvement process. In a regular game it takes a couple of years of work to fully upgrade a shipyard.
"The upgrade to holks is a function of not only ships built or fleets repaired, but of time and the rate of money spent in that time period. In the beginning, shipbuilds are slow. A second order will hasten the launch date by several days. A third order in the queue will shave another few days off. Four seems to be the maximum. Repairs will also hasten the process of launches, and of ability to extend the ships. Smash a number of pirate vessels to single digits, capture and repair them. Money spent plus shipbuilds all divided by time passed is the equation." - Baltic Trader |
Upgraded shipyards also build and repair ships faster. The work speed of a shipyard (or Repair Dock) is indicated by the number of lanterns on the dock.
Improved shipyards have a different appearance:
Lack of activity will cause the opposite - repairs and building times will increase (which will be reflected by the number of lanterns).
Tip: The easiest way to upgrade a stale shipyard is to order a large number of ships (around 40 snaikkas, or 10 hulks if they are available).
Tip: It's also possible to place large convoys for repair (after running them through storms on purpose). This way the shipyard can be upgraded in just a few months. It can be useful if you need faster repairs for a new convoy route, for example.
Building Contracts
Here you can order a ship. You will see a list of possible ship types, the required materials and the construction time (note that the indicated construction time is not very accurate).
List of Contracts and Repairs
Here you can see the queue of ships and repairs that you ordered earlier, and cancel them. Repairs can be canceled at any time. Ship construction can only be canceled if the construction has not started yet.
Improve Ship
Improving a ship to a Level 2 or Level 3 version will increase (or add) weapon slots and hitpoints, at a cost of load capacity.
Ship's Name
This tab allows you to change the name of a ship. This is useful for organizing purposes, players come up with many creative naming conventions that help them keep better track of the ships in their vast fleets.
Some also claim that this will help in avoiding a piracy fine