The power savers you see advertised absorb spikes in the power system and deliver current smoothly. They work on the principle of ‘power factor correction‘, which happens in inductive loads.
In inductive loads the current waveform lags behind the voltage and the effect is to consume more power than the rated watts of the appliance. It’s particularly noticeable in fridges and Air Conditioning.
Electronic circuits inside the power saver, mostly capacitors, bring the current waveform back into line and so saving power.
For some appliances the savings will be very small, but as most home appliances are inductive (have copper coils inside), these devices will save power for most applications.