Tip-enhanced Raman spectroscopy (TERS) exhibits new selection rule and sub-nanometer spatial resolution, which is attributed to the plasmonic near-field confinement. Despite recent advances in simulations of TERS spectra under highly confined fields, a simply physical mechanism has remained elusive. In this work we show that single-molecule TERS images can be explained by local sub-molecular density changes induced by the confined near-field during the Raman process. The local sub-molecular density changes determine the spatial resolution in TERS and the gradient-based selection rule. Using this approach we find that the four-fold symmetry of meso-tetrakis(3,5-di-tert-butylphenyl)porphyrin (H2TBPP) TERS images observed in experiments arises from the combination of degenerate normal modes localized in the functional side groups rather than the porphyrin ring as previously considered. As an illustration of the potential of the method, we demonstrate how this new theory can be applied to microscopic structure characterization.