This is an extended faucet handle that allows the user to shut off the water with their elbow. This makes it easy to shut off the water while you are scrubbing your hands with soap. This saves water. You can then use your elbow to turn the water back on to rinse your hands and then turn the water off when you're done. This keeps your clean hands from touching a potentially contaminated faucet handle.
Only the hot water handle is shown to demonstrate the difference it makes. Please note that this handle is not universal and will have to be adapted for different makes and models of faucets.