This Letter provides information on the spatial and temporal structure of periodic eruptions observed in magnetically confined laboratory fusion plasmas, called edge-localized modes (ELMs), and highlights similarities with solar eruptions. Taken together, the observations presented in this Letter provide strong evidence for ELMs being associated with a filamentlike structure. These filaments are extended along a field line, are generated on a 100 micros time scale, erupt from the outboard side, and connect back into the plasma. Such structures are predicted by a theoretical model based on the "ballooning" instability, developed for both solar and tokamak applications.