Ship construction refers to the part of overall production that is used to manufacture ships of all classes at shipyards.
History
The 
expansion drastically changed the economy, making the explanation below obsolete. The merger of the Crusade UI into the base game renamed "manufacturing" to "construction" and "military" to "ship".
Generation
Ship construction is allocated by assigning parts of your economy to construction, and then setting the social/ship construction slider. Unlike social construction, modifiers that affect only ship construction are extremely rare. This means that most important ways of enhancing ship construction are those that increase your overall construction.
Planetary sponsors
One difference between ship and Social production is the fact that up to five planets are able to combine their ship output at a single shipyard.
Only limit to this is the diminishing returns on long distances between the planets, or sponsors, and the shipyard. The link is at full capacity when the distance between the shipyard and sponsor is six tiles or less, and the percentage of the original ship production that is available to the shipyards starts to drop as the distance increases after that.
Certain race traits and ideologies can decrease the effects of distance on the production.