In the Bohr model the electrons move around the central nucleus on certain specified circular trajectories. On these trajectories the wave associated with the electron has to be a standing wave, that is a closed wave (the beginning of the wave has to connect with the end of the wave). Because of this condition (of standing wave) only certain trajectories are allowed. When the electrons jumps from one allowed trajectory to another it emits (or absorbs) a photon of a certain (given) frequency. (If the electrons jumps on a lower orbit it emits a photon). Because there are allowed only certain trajectories, this gives (on electron jumps) only certain alowed frequencies. We say that the spectra is discrete.
