hmm...on a lot of Medela pumps, there's a similar membrane, but it's smaller than the size of a dime. In those case, the membrane is very important as it's one of the parts that creates the suction.
You may want to try looking around the Medela site and see if you can find it on their site and perhaps it will have information on what it goes with and how to use it. Good luck!
It looks like an attachment for one of the hospital grade medela pumps (sympony). That's the part that attaches to the pump itself- you open up the top and there's a spot for each of the large circular pieces.