What is Born–Oppenheimer approximation?

In the Born–Oppenheimer approximation, the electronic Schrödinger equation is solved for nuclei held fixed at positions $\mathbf R$,

and the nuclei then move in the potential $E_{\mathrm{el}}(\mathbf R) + V_{\mathrm{nn}}(\mathbf R)$, the electronic energy plus the repulsion of the nuclei.