The magneto-optical Faraday effect is studied in one-dimensional magnetophotonic crystals (MPCs). Mechanisms of a strong enhancement of the Faraday rotation at the edges of the photonic band gap are considered. High difference of refractive indexes of bismuth-substituted yttrium iron garnet (Bi:YIG) and SiO₂ layers provides a strong spatial localization of the optical field in Bi:YIG layers, which leads to manifold Faraday rotation enhancement at the photonic band edges. The Faraday rotation angle in the finite MPCs appears to be a nonlinear function of the total thickness of magnetic material in the stack that can be interpreted as the nonlinear Verdet law. Relation between the enhancement of the Faraday rotation and localization of optical field in magnetic layers is treated as a Borrmann-type effect. This relation shows that the Faraday rotation can be considered as a measure of the density of photonic states trapped within Bi:YIG layers.