Dielectric breakdown in air induced by a train of subnanosecond laser pulses was found to occur as a sequence of strong point explosions, with each pulse producing breakdown at a different spot. The angular dependence of the scattered laser light was found to be due to the reflection and diffraction from the breakdown spots which were approximately spherical with diameters of about 9 \ensuremath{\mu}m. For atmospheric breakdown, analysis of results indicates that a plasma density as high as 7\ifmmode\times\else\texttimes\fi{}${10}^{20}$ ${\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{n}\mathrm{s}/\mathrm{c}\mathrm{m}}^{3}$ was created in the breakdown region.