How can a capacitor works as a power saver?

A capacitor does not and cannot work as a 'power saver' or, more-accurately, 'energy saver'.

However, a capacitor can be used to reduce the power factor of a load. Reducing power factor, though, has absolutely no effect whatsoever on the amount of energy consumed by that load and will not reduce the energy bill for a residential consumer such as you or me.

What reducing power factor does is to reduce the load current which, in turn, will reduce the amount of copper that must be provided by the utility company, in terms of its cables and Transformers. So power factor 'improvement' can save the utility company money, by allowing it to use smaller cables and transformers to supply any given load.