Do you know what this thin metal wire is? It's attached to the water line in my garage. It looks like it was cut off at the end. I can't see where the other end of the cable ends up - it runs behind the wall.
It's your electrical service ground, comes from your panelbox.
First, that's hardly "thin" by house wiring standards. It looks like #8 or larger.
You've shown us one end of the wire. Check out the other end. It probably goes to your breaker box and is ultimately tied to the center tap of the transformer feeding AC power into your house.
If so, this is the grounding wire for your house's electrical system. It looks like it is connected to the copper water feed pipe into your house. That pipe goes underground and is a good earth connection. Since it was already present, it was used as the ground for your house instead of a separate stake driven into the ground for that purpose.
The two clamps are to provide a redundant connection to the copper pipe.