Why is there a copper wire attached to this water pipe?
In the UK, current regulations require all metallic pipework be connected electrically, this is called equipotential bonding. 



(images from electrician2hire)

By law, the connections must be labelled (typically with an embossed metal label)



I believe current regulations require this equipotential bonding in every room that has metal pipework. This helps guard against loss of earth bonding when a small section of copper pipe in between locations is replaced by plastic pipe. The clamps must be in a place where they can be inspected - which rules out hiding them under the floor or behind plasterboard (drywall.)