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We report on the optical properties from terahertz (THz) to Near-Infrared (NIR) of the layered magnetic compound CrI3 at various temperatures, both in the paramagnetic and ferromagnetic phase. In the NIR spectral range, we observe an insulating electronic gap around 1.1 eV which strongly hardens with decreasing temperature. The blue shift observed represents a record in insulating materials and it is a fingerprint of a strong electron-phonon interaction. Moreover, a further gap hardening is observed below the Curie temperature, indicating the establishment of an effective interaction between electrons and magnetic degrees of freedom in the ferromagnetic phase. Similar interactions are confirmed by the disappearance of some phonon modes in the same phase, as expected from a spin-lattice interaction theory. Therefore, the optical properties of CrI3 reveal a complex interaction among electronic, phononic and magnetic degrees of freedom, opening many possibilities for its use in 2-Dimensional heterostructures. [ABSTRACT FROM AUTHOR]