A very robust stylized fact has recently emerged concerning the distribution of growth rates of manufacturing business firms. We briefly review past analysis and present new evidence on this topic from the Italian Manufacturing Industry. We then propose a very simple model that, under rather general assumptions, provides an excellent explanation for the observed regularities. The model is based on a very simple stochastic process describing the random partition of a number of ``business opportunities'' among a population of identical firms. A theoretical result is presented for the limiting case in which the number of firms and opportunities go to infinity. Moreover, using simulations, we show that even in a moderately small industry the agreement with asymptotic results is almost complete.