Slater's rules are an attempt to lump the effect of all other electrons on the wavefunction, and thereby other properties such as energy, of an electron (described by a hydrogen-like wavefunction). The effect of electron-electron repulsion is modeled indirectly by saying that inner shell electrons effectively screen the attractive nuclear charge sensed by electrons further away from the nucleus. For simplicity screening is modeled as a one-sided effect: electrons further from the nucleus are not expected to significantly shield those closer to it, since an outer electron is close to the nucleus less frequently than an inner one (or, using more accurate language, the density near the nucleus of the outer electron is lower).
Slater's rules amount to a method of estimating appropriate exponents in a hydrogenic approximation of the electron wavefunction. They are semi-empirical, useful as a guide to explain why certain trends are observed, and fit data because they contain "fudge-factors" (parameters obtained from fits to data, not from fundamental theory). Still, that they work at all indicates what amazing insight Slater had in selecting the shape of the function and using the method to predict a number of atomic properties across the periodic table. If you haven't you should look at his original paper (Ref. 1), it's impressive and accessible. This is also fairly well explained in a Wikipedia article.
- Slater, J.C. Phys. Rev. 36 (1): 57–64. doi:10.1103/PhysRev.36.57.