The CRISPR (clustered regularly interspaced short palindromic repeats)-Cas9 system recently emerged as a transformative genome-editing technology that is innovating basic bioscience and applied medicine and biotechnology. The endonuclease Cas9 associates with a guide RNA to match and cleave complementary sequences in double stranded DNA, forming an RNA:DNA hybrid and a displaced non-target DNA strand. Although extensive structural studies are ongoing, the conformational dynamics of Cas9 and its interplay with the nucleic acids during association and DNA cleavage are largely unclear. Here, by employing multi-microsecond time scale molecular dynamics, we reveal the conformational plasticity of Cas9 and identify key determinants that allow its large-scale conformational changes during nucleic acid binding and processing. We show how the "closure" of the protein, which accompanies nucleic acid binding, fundamentally relies on highly coupled and specific motions of the protein domains, collectively initiating the prominent conformational changes needed for nucleic acid association. We further reveal a key role of the non-target DNA during the process of activation of the nuclease HNH domain, showing how the nontarget DNA positioning triggers local conformational changes that favor the formation of a catalytically competent Cas9. Finally, a remarkable conformational plasticity is identified as an intrinsic property of the HNH domain, constituting a necessary element that allows for the HNH repositioning. These novel findings constitute a reference for future experimental studies aimed at a full characterization of the dynamic features of the CRISPR-Cas9 system, and-more importantly-call for novel structure engineering efforts that are of fundamental importance for the rational design of new genome-engineering applications.