The physical mechanism of fast flame acceleration in tubes with obstacles is explained by recognizing that delayed burning between the obstacles creates a powerful jet flow which drives the acceleration. It is demonstrated theoretically and computationally that this mechanism is unlimited in time and independent of the Reynolds number, and it is much stronger and qualitatively different from the classical Shelkin mechanism of flame acceleration due to wall friction. As long as the gas compression is weak, the flame accelerates exponentially, with an enormous acceleration rate. We present formulae describing evolution of the flame tip, as well as its velocity and acceleration rate. Furthermore, it is shown that flames accelerate noticeably stronger in the axisymmetric cylindrical geometry as compared to the planar one.