Acoustically sensitive emulsion droplets composed of a liquid perfluorocarbon have the potential to be a highly efficient system for local drug delivery, embolotherapy, or for tumor imaging. The physical mechanisms underlying the acoustic activation of these phase-change emulsions into a bubbly dispersion, termed acoustic droplet vaporization, have not been well understood. The droplets have a very high activation threshold; its frequency dependence does not comply with homogeneous nucleation theory and localized nucleation spots have been observed. Here we show that acoustic droplet vaporization is initiated by a combination of two phenomena: highly nonlinear distortion of the acoustic wave before it hits the droplet and focusing of the distorted wave by the droplet itself. At high excitation pressures, nonlinear distortion causes significant superharmonics with wavelengths of the order of the droplet size. These superharmonics strongly contribute to the focusing effect; therefore, the proposed mechanism also explains the observed pressure thresholding effect. Our interpretation is validated with experimental data captured with an ultrahigh-speed camera on the positions of the nucleation spots, where we find excellent agreement with the theoretical prediction. Moreover, the presented mechanism explains the hitherto counterintuitive dependence of the nucleation threshold on the ultrasound frequency. The physical insight allows for the optimization of acoustic droplet vaporization for therapeutic applications, in particular with respect to the acoustic pressures required for activation, thereby minimizing the negative bioeffects associated with the use of high-intensity ultrasound.