The nearby supernova search is on ongoing effort by the LBNL to finding supernovae with a redshift of less than 0.1, reshift being a measure of ditsance. A redshift of 0.1 translates to about 500 Million Light Years.
Supernova are interesting astronomical phenomenon for several reasons.
Chiefly a supernova is a calibrateable distance measure. It is currently very difficult to find an accurate measure of the distance to a far away object, such as a distance galaxy. However when a supernova goes off it shines as brightly as a galaxy. Accurate measurements of the supernova can then be used to find the distance to the galxy that it resides in. Using this information the Hubble constant can then be accurately determined.