We measure moments of the galaxy count probability distribution function in the Two-degree Field Galaxy Redshift Survey (2dFGRS). The survey is divided into volume-limited subsamples in order to examine the dependence of the higher-order clustering on galaxy luminosity. We demonstrate the hierarchical scaling of the averaged p-point galaxy correlation functions, , up to p= 6. The hierarchical amplitudes, , are approximately independent of the cell radius used to smooth the galaxy distribution on small to medium scales. On larger scales we find that the higher-order moments can be strongly affected by the presence of rare, massive superstructures in the galaxy distribution. The skewness S3 has a weak dependence on luminosity, approximated by a linear dependence on log luminosity. We discuss the implications of our results for simple models of linear and non-linear bias that relate the galaxy distribution to the underlying mass.