Factories are used to build more advanced materials and constructions from the basic materials you have collected through the game.

Clicking the manufactured block type or construction you want and then clicking the select box at the bottom right corner will give you a list of all materials needed( and if you don't have the materials you need to create the block/construction it will tell you how many of what you are missing in red ).

Select the amount you want to make with the up/down arrows on the right. Clock go to create and the blocks/constructions will be placed into your inventory.