That looks like it broke off of a Champion valve adapter. What kind of valves do you have in your yard? Maybe take a pic.
It holds the seat washer on so eventually the valve will fail or maybe it's been replaced already because once that part breaks off the valve will have problems. It might get stuck on or it might sound like it wants to come on but it's not.
The good news is the part got stuck in a faucet and not the valves. That means the hose bib might be at the end of the line so you can flush any debris out there.
Maybe after repairing a valve if needed, you can unscrew the faucet and flush it out.
This post has been edited 2 times, last edit by "mrfixit" (Nov 10th 2017, 11:50pm)