Crystalline surfaces of gold are chemically inert, whereas nanoparticles of gold are excellent catalysts for many reactions. The catalytic properties of nanostructured gold have been connected to increased binding affinities of reactant molecules for low-coordinated Au atoms. Here we show that the high reactivity at these sites is a consequence of the formation of σ-holes, i.e., maxima in the surface electrostatic potential (VS,max), due to the overlap of mainly the valence s-orbitals when forming the bonding σ-orbitals. The σ-holes are binding sites for Lewis bases, and binding energies correlate with the magnitudes of the VS,max. For symmetrical Au clusters, of varying sizes, the most positive VS,max values are found at the corners, edges, and surfaces (facets), decreasing in that order. This is in agreement with the experimentally and theoretically observed dependence of catalytic activity on local structure. The density of σ-holes can explain the increasing catalytic activity with decreasing particle size for other transition metal catalysts also, such as platinum.