When quenched rapidly beyond their glass transition, colloidal suspensions fall out of equilibrium. The pace of their dynamics then slows down with the system age, i.e., with the time elapsed after the quench. This breaking of time translational invariance is associated with dynamical observables which depend on two time-arguments. The phenomenology is shared by a broad class of aging systems and calls for an equally broad theoretical description. The key idea is that, independent of microscopic details, aging systems progress through rare intermittent structural relaxations that are de-facto irreversible and become increasingly harder to achieve. Thus, a progression of record-sized dynamical barriers are traversed in the approach to equilibration. Accordingly, the statistics of the events is closely described by a log-Poisson process. Originally developed for relaxation in spin glasses, this theory also allows us to describe experimental colloidal data in great detail. Here we demonstrate this by performing a statistical analysis of rare events in experimental data describing an aging colloidal system.