The CRISPR/Cas9 complex, a bacterial immune response system, has been widely adopted for RNA-guided genome editing and transcription regulation in applications such as targeted genome modification and site-directed mutagenesis. However, the physical basis for its target specificity is not fully understood. In this study, based on a statistical mechanical analysis for the whole ensemble of sgRNA-target complex conformations, we identify a strong correlation between Cas9 cleavage efficiency and the stability of the DNA-RNA (R-loop) complex structures, with a Pearson correlation coefficient ranging from 0.775 to 0.886 for the tested systems. The finding leads to quantitative insights into important experimental results, such as the greater Cas9 tolerance to single-base mismatches in PAM-distal region than to PAM-proximal region and the high specificity and efficiency for shorter protospacers. Moreover, the results from the genome-wide off-target assessments, compared with other off-target scoring tools, indicate that the statistical mechanics-based approach provides more reliable off-target analyses and sgRNA design. To facilitate the genome engineering applications, a new web-based tool for genome-wide off-target assessment is established.