What is the meaning of inverter on air-conditioing?
They are using the term "inverter" to describe the conversion of Alternating Current to Direct Current and then back to Alternating Current.

Industry uses a device called a Variable Frequency Drive to control the speed of Alternating Current motors for various purposes.

These VFD devices have become inexpensive enough to now be used to control light commercial and residential devices such as air conditioners and well pumps.

This use of a VFD in an "inverter" air conditioner makes it much more efficient than a non-inverter air conditioner since it can run at slower speed for lower demand. An old style air conditioner is either on at full speed or off. There is no speed control.

If you are updating your air conditioner then inverter technology will pay for itself over the life of the unit and save you money.

Read the article here for an overview.

Good luck!