Aims: With the afterglow of GRB 100621A being the brightest detected so far in X-rays, and superb GROND coverage in the optical/near-infrared during the first few hours, an observational verification of basic fireball predictions seemed possible. Methods: In order to constrain the broad-band spectral energy distribution of the afterglow of GRB 100621A, dedicated observations were performed in the optical/near-infrared with the 7-channel Gamma-Ray Burst Optical and Near-infrared Detector (GROND) at the 2.2 m MPG/ESO telescope, in the sub-millimeter band with the large bolometer array LABOCA at APEX, and at radio frequencies with ATCA. Utilizing also Swift X-ray observations, we attempt an interpretation of the observational data within the fireball scenario. Results: The afterglow of GRB 100621A shows a very complex temporal and spectral evolution. We identify three different emission components, the most spectacular one causing a sudden intensity jump about one hour after the prompt emission. The spectrum of this component is much steeper than the canonical afterglow. We interpret this component using a two-shell collision prescription after the first shell has been decelerated by the circumburst medium. We use the fireball scenario to derive constraints on the microphysical parameters of the first shell. Long-term energy injection into a narrow jet seems to provide an adequate description. Another noteworthy result is the large (AV = 3.6 mag) line-of-sight host extinction of the afterglow in an otherwise extremely blue host galaxy. Conclusions: Some GRB afterglows have shown complex features, and that of GRB 100621A is another good example. Yet, detailed observational campaigns of the brightest afterglows promise to deepen our understanding of the formation of afterglows and the subsequent interaction with the circumburst medium.