The Bohr model (Bohr model of the atom or Rutherford-Bohr model) is a dated but still useful model of atoms. It incorporates the familiar idea of electrons traveling in circles, orbiting around the nucleus, but assumes the length of the orbit path is quantized, i.e., can only take certain values. (Technically, it is the angular momentum that must be an integer multiple of a constant that incorporates the Planck constant.) It also assumes that photons are created or absorbed as electrons shift from one orbit to another, according to the energy difference in kinetic and potential energy. The model correctly predicts the frequency of photons in hydrogen spectral lines (Lyman series, Balmer series, etc.) but the eventual quantum theory that replaced it correctly predicts much more. (Though the word orbit is still used for electrons in more modern quantum theory, such an orbit is no longer take as the electron actually moving in circles around the nucleus in the manner of astronomical objects such as a planet orbiting a star.)
The Bohr radius is the radius of the electron orbit of the ground state (smallest possible orbit) of hydrogen as per the Bohr model. It can be used as a rough approximation of the size of an atom for some purposes.