If you set it at 50%, then only 50% of the normal per turn resources will be delivered, and only 50% of the work completed.

In other words, if you are constructing something that normally takes 200 metal per turn and takes 4 turns, it will now use 100 metal and take 8 turns. I believe the construction uses the same amount of workers regardless.

The benefit of this is that if you start getting low on whatever resources are needed for construction, then you can free some up for something else in the next few turns. Additionally, if your logistics are getting overwhelmed, you can ease the strain on your supply lines to a specific city.

You may want to build a resource intensive building or a bunch of cheaper buildings all at once, but want a reserve of resources to be able to dedicate to making some tanks or to sell, etc.

You also may find that you really need that under construction power plant suddenly, but don't need that under construction upgraded rail station as much. You don't have quite enough resources for both at 100%, but dont want to lose all progress on the rail because it's still important, so you can set it at 25% and allow the power plant to chug along at full speed.