Verdet constant is one of the key parameters to characterize the material magneto-optical properties, and dependent on wavelength and temperature. In order to thoroughly analyze the influence mechanisms of the incident wavelength and temperature on the Verdet constant and then uncover its essence, both the advantages and disadvantages of the classical electronic dynamics theory and quantum theory are discussed on account of basic theories and test data. However, neither of the two theories can be separately used to fully explain the Verdet constant and the correlative test data. Therefore, based on the essential property of the magneto-optical effect, the interactions between the incident light and magnetic matter in a magnetic field are studied, and then a hypothesis which suggests that the Faraday effect result from the combination of various factors is proposed. Furthermore, a theory of wave-transition contribution to the Verdet constant is deduced by adopting the theory of wave-particle duality. That is, the Faraday effect is caused by two different contributions simultaneously. One is the wave contribution, which is the interaction between the wave aspect of light and the magneto-optical medium, and the other refers to the transition contribution, which comes from the electronic transition. When the light enters into a deflection angle, the wave contribution is positive while the transition contribution is negative. In a diamagnetic material, since the wave contribution is greater than the transition contribution, the diamagnetic Verdet constant is positive while in a paramagnetic material, on the contrary, the transition contribution is much larger than the wave contribution, so the paramagnetic Verdet constant is negative. According to the above-mentioned theory, the diamagnetic Verdet constant model and the paramagnetic Verdet constant model are proposed by combining the two parts together. Taking the typical diamagnetic material ZF1 and the typical paramagnetic terbium gallium garnet for example, the influences of the incident wavelength and the temperature on the Verdet constant are analyzed, and the deduced theory together with the corresponding models is tested and verified by analyzing the relevant parameters and the test data. Accordingly, the research turns out that the theoretical results correspond to the real values, which proves the rationality of the hypothesis and the authenticity of the deduced theory. Compared with the traditional theories, the wave-transition contribution theory and its model are superior in the sense of precisely describing the material Verdet constant.