The most common explanation of how lifters work is that they use ion wind.

An ion is an atom or molecule with a negative charge (having gained at least one electron), or a positive charge (having lost at least one electron).

An ion wind occurs when molecules in the air, get close enough to the positively charged wire, and are robbed of an electron, leaving them with a positive charge. They are then repelled from the wire and attracted to the foil electrode, where they gain back their lost electron and once again have a neutral charge. Due to the acceleration, the molecules move rapidly out through and past the lifter, forcing the craft upwards.