The scope and sophistication of ecological theory for social insects have greatly increased in the last half century. However, there remains an absence of theoretical work linking the population dynamics within a colony to the dynamics of a population of colonies. Many important ecological and evolutionary questions cannot be adequately addressed without a theory of population dynamics that incorporates the hierarchy of individuals within colonies and colonies within a population. For example, differences in growth rates of two populations can result from differences in intra-colonial birth and death rates or from differences in colony-level demography such as time to swarming. We present an analytical model that provides a simple, robust, and predictive theory for the population dynamics of social insects. The model was developed with particular reference to honeybees Apis mellifera and may be most applicable to similar species (e.g. monogynous eusocial insects). However, our main goal is to elucidate the hierarchical interaction of individual and colony processes in shaping population dynamics. Our model explicitly describes and links demographic dynamics for the different levels in the hierarchy (individuals, colonies, population). We illustrate the application of the model by analyzing the effects of life history traits such as worker lifespan and size at swarming on the growth rate of populations. After illustrating the insights that can be gained with the relatively simple model, we show that the theory can straightforwardly accommodate more realistic and complex biological details.