Relativistic high-order harmonic generation by plasma mirrors is for the first time generally explained in the framework of coherent synchrotron emission of nanoscale electron bunches incorporating impacts of the bunch width and shape. Under most conditions, the emission spectrum decays as a power of frequency with exponent −p up to a roll off set by the width of the emitting electron bunch. The spectrum then approximately decreases as a power-law with exponent −p−2, until an exponential falloff at a frequency proportional to the cube of the electron Lorentz factor. The initial power-law exponent p appears limited to around 4/3. The theoretical limiting efficiency of the process allows for 1-TW peak power to be produced for 1-keV photons using a plasma mirror driven by a 20-PW 800-nm-wavelength laser.