Neurons in higher cortical areas, such as the prefrontal cortex, are often tuned to a variety of sensory and motor variables, and are therefore said to display mixed selectivity. This complexity of single neuron responses can obscure what information these areas represent and how it is represented. Here we present a dimensionality reduction technique, demixed principal component analysis (dPCA), that decomposes population activity into a few components. In addition to systematically capturing the majority of the variance of the data, dPCA also exposes the neural representation in terms of task parameters such as stimuli, decisions, or rewards. To illustrate our method we reanalyze population data from four datasets comprising different species, different cortical areas and different experimental tasks. In each case, dPCA provides a concise way of visualizing the data that summarizes all the relevant features of the population response in a single figure. In addition, dPCA highlights several important and seemingly universal features of the population activity in prefrontal cortex; e.g. that most of the neural activity is not related to any of the controlled task parameters, such as stimuli or decision; or that there are no well-separated functional clusters of cells.