An increase in Social Construction improves how fast you can build improvements (buildings, wonders, terraforming, etc) on your planet.  An increase in Shipyard Construction increases how fast you can build ships.  An increase in Wealth or tourism increases how much money your planet generates.  An increase in research ... well, you get it by now.

The critical factor in all of these is what is called Raw Production.  Raw Production is calculated from the square root of your population, plus bonuses from asteroid mining bases, ideology choices, certain techs, and approval.  If your Raw Production is X, then your base social construction, ship construction, research, and income is also X.  You cans see this by mousing over those areas on the planet screen and observing the tooltips.

A planetary improvement normally provides some benefit to one or more of these areas (All Construction improves both Social and Ship Construction), plus adjacency benefits.  Adjacency increases the effect of any improvement built on an adjoining tile.  This matters more for some improvements than others.  The Computer Core, for examples, adds +1 Research per level, so an adjacency bonus of +3 research from a building next to the Computer Core raises your research by +3, while +3 levels to a Xeno Research lab will raise your research by 15% (5% per level).  Some buildings only increase 1% per level.

Some tiles provide bonuses to the improvements built on them plus adjacency bonuses to the surrounding tiles.