The Federal Reserve is a privately owned entity, it has its stash of gold in New York and the actual government has its smaller stash of gold in Fort Knox.
Let's say that Apple sees the price of its stock drop to something that it thinks is unreasonably low. They may choose to spend some of their cash on hand to buy back some of their stock. This is a wise investment that shareholders would applaud - Apple is getting a good deal.
Same deal with the Federal Reserve. Federal Reserve notes are nominally liabilities for the Fed, and are much like the concept of Apple stock. If the Fed notices the price of the dollar drops, it's in their best interest to trade some of their holdings to buy back some dollars.