Superconductivity is a fascinating example of how "more is different". It is due to electrons binding into bosonic Cooper pairs, which exhibit coherent behavior across a macroscopic sample. Finding the mechanism responsible for this binding is one of the more difficult tasks of condensed matter physics. For conventional superconductors the solution was given by the BCS theory as being due to exchange of phonons. For the cuprate high-Tc superconductors a widely-accepted explanation is still missing despite intense effort. The recently discovered Fe-based high-Tc superconductors pose now a new challenge. We present here a quantum mechanical theory for pnictides describing the influence of the large electronic polarizability of the heavy anions. We demonstrate that its inclusion results in electronic polarons as the low-energy quasi-particles and also unveils a pairing mechanism for these electronic polarons.