We present a detailed study of the brighter ($> 4sigma$ detections) sources in the 170$mu$m FIRBACK northern N1 ISO survey, with the help of complementary data in the optical, radio, and mid-IR domain. For 82% of them, an optical galaxy counterpart is identified, either as the unique source of the IR emission, or as part of a multiple identification. With less than 15% of AGNs, these sources are essentially local, moderate starbursters with a dominating cold dust component. and represent a population of cold galaxies rather neglected up to now. Their colours do not match those of the far-IR Cosmic IR Background (CIB), to which they contribute less than 5%. The bulk of the sources contributing to the CIB is thus to be searched for in more distant galaxies, possibly counterparts of the fainter FIRBACK sources still under study. These bright, local, galaxies however play an important role in the evolution of IR galaxies: they dominate the number counts at high 170 $mu$m fluxes, and represent half of the contribution at 250 mJy. Although not particularly massive (typically M*), they form more stars than a typical spiral galaxy and many are bulge dominated, that could represent the remnant of a former merger. The fainter part of this population may represent the missing link with the higher-z sources found in sub-mm observations.