Intermittent or serrated plastic flow is widely observed in the deformation of bulk metallic glasses (BMGs) or other disordered solids at low temperatures. However, the underlying physical process responsible for the phenomena is still poorly understood. Here, we give an interpretation of the serrated flow behavior in BMGs by relating the atomic-scale deformation with the macroscopic shear band behavior. Our theoretical analysis shows that serrated flow in fact arises from an intrinsic dynamic instability of the shear band sliding, which is determined by a critical stiffness parameter in stick-slip dynamics. Based on this, the transition from serrated to nonserrated flow with the strain rate or the temperature is well predicted and the effects of various extrinsic and intrinsic factors on shear band stability can be quantitatively analyzed in BMGs. Our results, which are verified by a series of compression tests on various BMGs, provide key ingredients to fundamentally understand serrated flow and may bridge the gap between the atomic-scale physics and the larger-scale shear band dynamics governing the deformation of BMGs.