The knurled "pin" or anvil on the left is adjustable for various width chains. For example older 5-speed chains and track chains are wider than newer 8,9, 10 and 11-speed chains. You place the chain over the shelf to the left, adjust the anvil so it's snug against the chain and push out the pin with the screw press.

The other shelf is the "loosening shelf" and is used to slightly spread the chain to free up a tight link. It should not be needed with modern chains if the special joining pin (Shimano) or master link (most others) are used.