We study numerically the crystallization process in a supersaturated suspension of repulsive colloidal particles driven by simple shear flow. The effect of the shear flow on crystallization is two-fold: while it suppresses the initial nucleation, once a large enough critical nucleus has formed its growth is enhanced by the shear flow. Combining both effects implies an optimal strain rate at which the overall crystallization rate has a maximum. To gain insight into the underlying mechanisms, we employ a discrete state model describing the transitions between the local structural configurations around single particles. We observe a time-scale separation between these transitions and the overall progress of the crystallization allowing for an effective Markovian description. By using this model, we demonstrate that the suppression of nucleation is due to the inhibition of a pre-structured liquid.