As described in the previous posts. it is primarily a safety function.
It can be thought of in the same way as an "Isolated DC Power Supply" in that neither pos or neg is grounded (Earthed). Obviously in AC the Plus and Minus are changing at 50 or 60 Hz.
As Bdunham7 already pointed out. If all the power is run thru a transformer, the power is essentially Floating or Isolated. Until you "reference" the Neg to GND.
Lab PS (DC and AC) use this arrangement. The Chassis can be grounded but neither pos or neg is referenced to GND.
There are implications both good and bad. Running everything thru an Isolation Transformer, the chassis is not Grounded.
In the US there were many radios that had no transformer and one end of the only two wire AC was attached to chassis. Also the two wire plugs were symmetrical. US at that time 110 V AC. I think a popular radio like this was an "All American 5" (5 valves), the heaters of the valves were also fed in series with the 110 AC. They could be a problem especially if operated on the kitchen sink.
Today, Oscilloscopes almost all have their Neg connected to GND, there are implications if you "float" a scope.
I think Benchtop Multimeters like HP 3456 have "Floating Inputs". Handheld Multimeters are floating because of the battery power.