A prediction of the standard Lambda cold dark matter cosmology is that dark matter (DM) haloes are teeming with numerous self-bound substructure or subhaloes. The precise properties of these subhaloes represent important probes of the underlying cosmological model. We use data from Via Lactea II and Exploring the Local Volume in Simulations N-body simulations to learn about the structure of subhaloes with masses 10(6)-10(11) h(-1) M circle dot. Thanks to a superb subhalo statistics, we study subhalo properties as a function of distance to host halo centre and subhalo mass, and provide a set of fits that accurately describe the subhalo structure. We also investigate the role of subhaloes on the search for DM annihilation. Previous work has shown that subhaloes are expected to boost the DM signal of their host haloes significantly. Yet, these works traditionally assumed that subhaloes exhibit similar structural properties than those of field haloes, while it is known that subhaloes are more concentrated. Building upon our N-body data analysis, we refine the substructure boost model of Sanchez-Conde & Prada (2014), and find boosts that are a factor 2-3 higher. We further refine the model to include unavoidable tidal stripping effects on the subhalo population. For field haloes, this introduces a moderate (similar to 20-30 per cent) suppression. Yet, for subhaloes like those hosting dwarf galaxy satellites, tidal stripping plays a critical role, the boost being at the level of a few tens of percent at most. We provide a parametrization of the boost for field haloes that can be safely applied over a wide halo mass range.