This is a fixing tool for our Large Press Studs, which have a 15mm cap size.
The round part of the tool is called an anvil and is used as a base to support the popper pieces, while the long handle is inserted into the tube of the popper and hit with a mallet to secure 2 pieces together around the leather. The anvil has a dent in one side, for use with the 'outside' half of the popper, and a flat side which you place uppermost when fitting the 'inner' half.
Don't worry, it's easier than it sounds!
Please note: This tool is not suitable for use with stainless steel press studs, which have their own tool.