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Audio equipment, analog and digital, works using varying voltages. A voltage is always measured between two points. It is meaningless to say that any one point in a circuit is at a certain number of volts, unless the reference point is also quoted.
For mains-powered equipment, that reference point is always Earth - capitalized because it is the planet Earth. The Earth is so big in comparison to any source of electricity - even the Hoover Dam, that all electrical currents that flow into it average out and the Earth's voltage is taken to be the ultimate zero volts reference.
So any voltage inside mains-powered equipment can be measured and quoted with reference to Earth. The chassis of the equipment will be connected to Earth to make sure it is at zero points, and the circuit will also be connected to Earth in order to supply the necessary zero volts reference to all of its elements, either through the chassis or separately.
'Ground' is often used as a synonym for Earth.
Connection to Earth is usually via the earth of the mains socket. This in turn is electrically connected to Earth, often through the plumbing system. However if this option is not available then a copper spike can be driven into the ground to provide the Earth connection. Whatever method is used, earthing or grounding can be more effective or less effective - a copper spike in dry soil or sand will not make a good connection to Earth.
A 'screen' is a metal sheath around a signal-carrying conductor. The idea is that any interference that might otherwise work its way into the conductor will be dispersed in the screen before it has chance to get through. This works a whole lot better if the screen is connected to Earth, so interference currents are swiftly and efficiently carried away.
Equipment that is mains-powered but not itself earthed at the mains connector nevertheless finds its earth through the other equipment to which it is connected. If used alone, then it is not earthed, but interference is dispersed within the metal parts of the chassis of the equipment. The same applies to battery-powered equipment.