ARCHIVELOG mode is a mode that you can put the database in for creating a backup of all transactions that have occurred in the database so that you can recover to any point in time
NOARCHIVELOG mode is basically the absence of ARCHIVELOG mode and has the disadvantage of not being able to recover to any point in time. NOARCHIVELOG mode does have the advantage of not having to write transactions to an archive log and thus increases the performance of the database slightly.
