Each production dialog box displays the production equation for that factory or mill. Red Xs near an item in the equation indicate shortages which prevent further use of an industry this turn.
Last turn, you were able to produce at your factories. This turn, depending on what resources you have gained, you may be able to produce at the mills as well.
Each industry has a listed capacity referring to the maximum amount of the end product that can be made in one turn. For example, even if you have plenty of iron, coal, and unused labor, you will not be able to produce more than 2 units of steel per turn in a capacity 2 steel mill.
Animations of the factories and mills on the screen let you know that they are in operation without requiring you to click on the center and view the dialog.