A developmental process, independent of morphogenetic (shape) change, that is required for the cerebellar granular layer to attain its fully functional state. The granular layer is the innermost layer of the cerebellar cortex. This layer contains densely packed small neurons, mostly granule cells. Some Golgi cells are found at the outer border. Granule neurons send parallel fibers to the upper molecular layer, where they synapse with Purkinje cell dendrites. Mossy fibers from the pontine nuclei in the white matter synapse with granule cell axons, Golgi cell axons and unipolar brush interneuron axons at cerebellar glomeruli in the granule cell layer.