Solubility follows law of "like" dissolves "like". Therefore, a non-polar molecule stays insoluble in polar solvent and solubilises into a non-polar solvent and vice-versa. Since I2 is non-polar and H2O is polar, therefore they are immiscible. Upon addition of KI, I2 forms KI−3 and becomes polar. Moreover, due to ion-dipole interaction between KI−3anion and water the solubility increases.