Heterolytic or ionic fission is the breaking of a covalent bond in such a way that one atom gets both of the shared electrons.
The word heterolytic comes from the Greek heteros, "different", and lysis, "loosening".
Heterolytic cleavage is most likely to occur in polar bonds. And the electrons will move toward the more electronegative atom.
If both atoms are originally uncharged, the process generates a cation and an anion.
An example is the heterolytic cleavage of the C-Br bond in t-butyl bromide.
Since Br is more electronegative than C, the electrons move to the Br. We get a t-butyl cation and a bromide anion.