Despite strong interest in the starburst (hereafter SB) phenomenon, the concept remains ill-defined. We use a strict definition of SB to examine the statistical properties of local SB and post-starburst (hereafter PB) galaxies. We also seek relationships to active galaxies. Potential SB galaxies are selected from the SDSS DR7 and their stellar content is analysed. We apply an age dependent dust attenuation correction and derive star formation rates (SFR), ages and masses of the young and old populations. The photometric masses nicely agree with dynamical masses derived from the H-alpha emission line width. To select SB galaxies, we use the birthrate parameter b=SFR/<SFR>, requiring b>=3. The PB sample is selected from the citerion EW(Hdelta_abs)>=6 A. Only 1% of star-forming galaxies are found to be SB galaxies. They contribute 3-6% to the stellar production and are therefore unimportant for the local star formation activity. The median SB age is 70 Myr, roughly independent of mass. The b-parameter strongly depends on burst age. Values close to b=60 are found at ages ~10 Myr, while almost no SBs are found at ages >1 Gyr. The median baryonic burst mass fraction of sub-L* galaxies is 5%, decreasing slowly with mass. The median mass fraction of the recent burst in the PB sample is 5-10%. The age-mass distribution of the progenitors of the PBs is bimodal with a break at log(M)~10.6 above which the ages are doubled. The SB and PB luminosity functions (hereafter LFs) follow each other closely until M_r~-21, when AGNs begin to dominate. The PB LF continues to follow the AGN LF while SB loose significance. This suggests that the number of luminous SBs is underestimated by about one dex at high luminosities, due to large amounts of dust and/or AGN blending. It also indicates that the SB phase preceded the AGN phase. We also discuss the conditions for global gas outflow caused by stellar feedback.
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