The shield should be "grounded" to the 0V or chassis or whatever the signal is going in to, it does not literally have to be connected to earth ground.
In such as a multimeter or portable device, the screening or shielding will divert any stray external signals to the 0V, rather than them getting through to the sensitive signal traces.
And also block any stray emissions from leaving that part of the device, in such as mobile phones.
(If the device is powered from AC mains, then the chassis or 0V should usually be connected to true earth / ground somewhere in the system).
With a signal cable, if the screen is not connected at either end, the effect will depend on what type of interference sources are nearby and how strong they are. It may make things slightly better than no screen at all - or it could make pickup worse, as anything close to the cable at just one point may allow noise to pass in over the entire cable length..