Power, i.e. watts, is ~ volts (V) * amperes (A). Powering a 600 watt fridge could be done with 240 V, 2.5 A, with 120 V, 5 A or with 5 V, 120 A. So there's no "magic", just a trade-off.
However, power loss as heat in electric wires is proportional to the current, measured in amperes. Though a 5 V battery could power the appliance, 120 A into the converter would require huge wires, about 50 times as thick as your house wiring. These bus bars would be very expensive, very heavy, hard to manipulate and difficult to connect.
In general, electric utilities and equipment manufacturers prefer to use the thinnest practical wire, so use higher voltages. Exceptions are in automotive applications, where 12 V batteries have a lower price (though many trucks use 24 V, now), and in shipboard use, where lowered voltage is considered safer in a wet environment.