The cerebellum is classically described in terms of its role in motor control. Recent evidence suggests that the cerebellum supports a wide variety of functions, including timing-related cognitive tasks and perceptual prediction. Correspondingly, deciphering cerebellar function may be important to advance our understanding of cognitive processes. In this paper, we build a model of eyeblink conditioning, an extensively studied low-level function of the cerebellum. Building such a model is of particular interest, since, as of now, it remains unclear how exactly the cerebellum manages to learn and reproduce the precise timings observed in eyeblink conditioning that are potentially exploited by cognitive processes as well. We employ recent advances in large-scale neural network modeling to build a biologically plausible spiking neural network based on the cerebellar microcircuitry. We compare our simulation results to neurophysiological data and demonstrate how the recurrent Granule-Golgi subnetwork could generate the dynamics representations required for triggering motor trajectories in the Purkinje cell layer. Our model is capable of reproducing key properties of eyeblink conditioning, while generating neurophysiological data that could be experimentally verified.