The funny star notation copies the contents of the one typeglob into another. Perl uses typeglobs to hold global variables -- such as filehandles. It's more or less the same thing as duping the filehandle as with your open call. (It has the same effect on the filehandle, but it copies the other slots of the typeglob. Don't worry if you don't understand that; it probably has no effect on your program.)

Unless you're printing to the log file from multiple processes or you need the data RIGHT NOW, don't worry about unbuffering it. If you do need to unbuffer it, select the filehandle, then set $|, then select the previously-selected filehandle -- or use a module such as IO::Handle.