Within each atom or ion there is a positively charged nucleus surrounded by a negative electron cloud.

To undergo ionic polarisation, a material must have an ionic structure i.e. it must be composed of cations and anions.

You may find it helpful to consider the simple case of a cation and anion, of equal and opposite charges, held together by an ionic bond. This ion pair already possesses a dipole moment before the application of an electric field, however the sum of dipole moments over the entire material (i.e. the net polarisation) may still be zero.

To gain a more general understanding of ionic polarisation, we must consider many ions at once.

Apply electric field

Some molecules possess a permanent dipole - there is always a separation of charge within the molecule, even in the absence of an electric field. The example shown here is H₂O.
Note that such permanent dipoles may also exist within ionic structures, e.g. crystals in which the cations are off-centred within the unit cells and do not coincide with the centre of negative charge.

Consider a material containing many such dipoles. In naturally non-polar materials like water, the dipoles are randomly arranged as a result of thermal motion. Therefore the dipole moments from different molecules cancel out and the net polarisation is zero.