Despite strong interest in the starburst phenomenon in extragalactic astronomy, the concept remains ill-defined. Here we use a strict definition of starburst to examine the statistical properties of starburst galaxies in the local universe. We also seek to establish links between starburst galaxies, post-starburst (hereafter postburst) galaxies, and active galaxies. Data were selected from the Sloan Digital Sky Survey DR7. We applied a novel method of treating dust attenuation and derive star formation rates, ages, and stellar masses assuming a two-component stellar population model. Dynamical masses are calculated from the width of the H-alpha line. These masses agree excellently with the photometric masses. The mass (gas+stars) range is approximately 10( exp 9) - 10(exp 11.5) solar mass. As a selection criterion for starburst galaxies, we use, the birthrate parameter, b = SFR/SFR, requiring that b is greater than 3. For postburst galaxies, we use, the equivalent width of Hdelta in absorption with the criterion EW (sub Hdelta_abs) is greater than 6 A. Results. We find that only 1% of star-forming galaxies are starburst galaxies. They contribute 3-6% to the stellar production and are therefore unimportant for the local star formation activity. The median starburst age is 70 Myr roughly independent of mass, indicating that star formation is mainly regulated by local feedback processes. The b-parameter strongly depends on burst age. Values close to b = 60 are found at ages approximately 10 Myr, while almost no starbursts are found at ages greater than 1 Gyr. The median baryonic burst mass fraction of sub-L galaxies is 5% and decreases slowly towards high masses. The median mass fraction of the recent burst in the postburst sample is 5-10%. A smaller fraction of the postburst galaxies, however, originates in non-bursting galaxies. The age-mass distribution of the postburst progenitors (with mass fractions is greater than 3%) is bimodal with a break at logM(solar mass ) 10.6, above which the ages are doubled. The starburst and postburst luminosity functions (LFs) follow each other closely until M(sub r ) (is) approximately -21, when active galactic nuclei (AGNs) begin to dominate. The postburst LF continues to follow the AGN LF, while starbursts become less significant. This suggests that the number of luminous starbursts is underestimated by about one dex at high luminosities, because of having large amounts of dust and/or being outshone by an AGN. It also indicates that the starburst phase preceded the AGN phase. Finally, we look at the conditions for global gas outflow caused by stellar feedback and find that massive starburst galaxies are susceptible to such outflows.