One of the greatest challenges in the field of semiconductor nanomaterials is to make trap-free nanocrystalline structures to attain a remarkable improvement of their optoelectronic performances. In semiconductor nanomaterials, a very high number of atoms is located on the surface and these atoms form the main source of electronic traps. The relation between surface atom coordination and electronic structure, however, remains largely unknown. Here, we use density functional theory to unveil the surface structure/electronic property relations of zincblende II-VI CdSe model nanocrystals, whose stoichiometry and surface termination agree with recent experimental findings. On the basis of the analysis of the surface geometry and the recent classification of the ligand surface coordination in terms of L-, X-, and Z-type ligands, we show that, contrary to expectations, most under-coordinated "dangling" atoms do not form traps and that L- and X-type ligands are benign to the nanocrystal electronic structure. On the other hand, we find clear evidence that Z-type displacement induces midgap states, localized on the 4p lone pair of 2-coordinated selenium surface atoms. We generalize our findings to the whole family of II-VI metal chalcogenide nanocrystals of any size and shape and propose a new schematic representation of the chemical bond in metal chalcogenide nanocrystals that includes explicitly the coordination number of surface atoms. This work results in a detailed understanding of the formation of surface traps and provides a clear handle for further optimization of colloidal nanocrystals for optoelectronics applications.