There are numerous indications that adsorbed particles on a surface do not desorb statistically, but that their spatial distribution is important. Evidence almost exclusively comes from temperature-programmed desorption, the standard method for measuring desorption rates. However, this method, as a kinetics experiment, cannot uniquely prove an atomic mechanism. Here we report a low-energy electron microscopy investigation in which a surface is microscopically imaged while simultaneously temperature-programmed desorption is recorded. The data show that during desorption of oxygen molecules from a silver single crystal surface, islands of oxygen atoms are present. By correlating the microscopy and the kinetics data, a model is derived that includes the shapes of the islands and assumes that the oxygen molecules desorb from the island edges. The model quantitatively reproduces the complex desorption kinetics, confirming that desorption is affected by islands and that the often used mean-field treatment is inappropriate.