The ultracold neutron (UCN) source at the Paul Scherrer Institute serves mainly experiments in fundamental physics. High UCN intensities are the key for progress and success in such experiments. A detailed understanding of all source parameters is required for future improvements. Here we present the UCN source components, elements of the neutron optics, the characterization of important related parameters like emptying times, storage times or transmission probabilities of UCN which are ultimately defining the UCN intensity delivered at the beamports. We also introduce a detailed simulation model of the PSI UCN source, used to analyze the measurements and to extract surface parameters.