We investigate the dynamics of a variety of jammed soft materials, including strongly attractive colloidal gels, concentrated surfactant phases, and charged platelets (Laponite). By using Time Resolved Correlation, a time-resolved dynamics light scattering technique, we show that, quite generally, the dynamics of these systems are strongly hetergogeneous in time, suggesting that they relax through discrete rearrangement events.. We measure the size of the rearrangement events using a novel space- and time-resolved light scattering method: quite surprisingly, we find that each event affects a volume much larger that the size of the system's constituent (particles or clusters). This finding is in stark contrast with simulations and experiments on supercooled fluids, where spatial correlations of the dynamics extend over a few particles at most.