This paper introduces local porosity distributions and local percolation probabilities as well-defined and experimentally observable geometric characteristics of general porous media. Based on these concepts the dielectric response is analyzed using the effective-medium approximation and percolation scaling theory. The theoretical origin of static and dynamic scaling laws for the dielectric response including Archie's law in the low-porosity limit are elucidated. The zero-frequency real dielectric constant is found to diverge as \ensuremath{\epsilon}\ensuremath{'}(0)\ensuremath{\propto}(1-\ensuremath{\varphi}${)}^{\mathrm{\ensuremath{-}}\mathrm{m}\ensuremath{'}}$ in the high-porosity limit, where \ensuremath{\varphi} denotes the porosity and m\ensuremath{'} is analogous to the cementation exponent. Model calculations are presented for the interplay between geometric characteristics and the frequency-dependent dielectric response. Three purely geometric mechanisms are identified, each of which can give rise to a large dielectric enhancement.