Why when you flush one toilet upstairs does the toilet downstairs make water noises?

Your water lines aren't properly isolated. when you flush the toilet and your water lines are refilling with water it can create water hammer. This is usually worse if your water pipes are either not properly supported or come in contact with wood joists or studs. You may also have very high water pressure which means a lot of air comes through with the water, try closing the water inlet a little. A loose washer on the shut off valve for the toilet can cause the jackhammer sound you describe.