It’s about protection from electric shock to the user of a device. Anything can fail, however the way risk can be reduced doesn’t have to be done one specific way.
Using an earth ground to an appliance or devices metal enclosure is one way. The wires and other parts inside already have basic insulation, sufficient clearances, etc to be generally safe even without an earth ground. However if something does go wrong anyway something inside with the potential to shock someone will contact the grounded chassis which causes a short to ground and a tripped circuit breaker, instead of electrocuting a person touching the device. These are called Class I devices, at least in the US
Double insulation is just that. A second layer of insulation is used to separate a user of a device from the high voltage. It also needs to be a different type, so you can’t just use a thicker layer around wires, which helps prevent both layers failing from the same cause. A plastic case is usually good enough to satisfy the requirement for this. For devices that don’t use too much power this is considered good enough extra protection that it may replace ground from a safety standpoint. This why many smaller power supplies and appliances like cell phone chargers, don’t need an earth ground. These would be a Class II devices. Still, after a certain power level, because of the increased risk you end up needing to use an earth ground anyway.
There’s also class III devices. These are things like laptops which are powered only be a low voltage external supply. Since the device itself doesn’t run on high voltage it doesn’t need either double insulation or earth ground for safety. Instead the responsibility for safety is shifted to the power adapter, does need double insulation.
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