Active log means which are current being used by the Database. As it is very critical for DB operation we used to have mirror in different disk. If one disk fails, the other will be used by DB. MIRRORLOGPATH is used to specify the mirror for active logs.
Log files are used in the circular fashion, if one log file is full then it will be archived to the location specified in the LOGARCHMETH1 and if this location fails then it will use the location specified in LOGARCHMETH2.
I hope it clarified