Electron screening is the reduction in the strength of an electric field surrounding a positively-charged particle (i.e., a nucleus) by nearby electrons. The structure of larger atoms (metals, in the language of astrophysics) is affected because electron orbits are affected by the electrons in smaller orbits. In this case, it is called the shielding effect.
Electron screening is also a factor in fusion rates in a plasma: the free electrons reduce the effective charge of the nuclei, enhancing the reaction by reducing the electric force between nuclei. In some types of stars, it is a significant factor in their energy production and nucleosynthesis.