Answer
The shield is necessary to prevent external magnetic fields from interfering with the small signal.
Work Step by Step
When an outgoing current and incoming return current travel along coaxial cables, it is like sending a current around a loop with zero area; one path is enclosed inside the other.
This cable may be sitting in an external magnetic field. If the external field were to change, normally this would change the flux in the circuit, inducing an emf and a current that could potentially overwhelm the valuable small signal that is being transmitted.
However, in this configuration with zero area, the magnetic flux remains at zero, so the effect of magnetic interference is eliminated.
