A developmental process, independent of morphogenetic (shape) change, that is required for the inferior olivary nucleus to attain its fully functional state. The inferior olivary nucleus is a capsule-shaped structure in the ventral medulla located just lateral and dorsal to the medullary pyramids. Neurons in the inferior olivary nucleus are the source of climbing fiber input to the cerebellar cortex; these neurons have been implicated in various functions, such as learning and timing of movements.