The single black wire is your ground wire for the bridge. The easiest way to ground the bridge is to solder the black wire to the spring claw in the rear cavity. There are other ways to achieve this, but the claw is most common in this scenario.

The blue wire is a coaxial wire meaning it has both a signal conductor and a shield (or ground in this case).
The white insulated lead in the centre goes to the "hot" lug of the output jack. The bare portion goes to the ground lug of the output jack.