The Jahn-Teller effect refers to the symmetry-lowering geometrical distortion in a crystal (or non-linear molecule) due to the presence of a degenerate electronic state.Usually, the Jahn-Teller distortion is not polar. Recently, GaV4S8 with the lacunar spinel structure was found to undergoes a Jahn-Teller distortion from cubic to ferroelectric rhombohedral structure at TJT = 38K. In this work, we carry out a general group theory analysis to show how and when the Jahn-Teller effect gives rise to ferroelectricity. On the basis of this theory, we find that the ferroelectric Jahn-Teller distort in GaV4S8 is due to the non-centrosymmetric nature of the parent phase and strong electron-phonon interaction related to two low-energy T2 phonon modes.Interestingly, GaV4S8 is not only ferroelectric, but also ferromagnetic with the magnetic easy axis along the ferroelectric direction. This suggests that GaV4S8 is a multiferroic in which an external electric field may control its magnetization direction.Our study not only explains the Jahn-Teller physics in GaV4S8, but also paves a new way for searching and designing new ferroelectrics and multiferroics.