The Dishwasher is an appliance which allows you to repair your tools, eg Pickaxe. To power the machine, you need to put Soapy Water or Super Soapy Water in the top right slot. Simply put your tools into the corrosponding slots on the GUI and hit the start button. Depending on the fuel you use, after every X amount of second(s), it will add one durability back onto your tool.
You can use the RecipeAPI to register custom tools from other mods to work with the Dishwasher.