A consistent backup is one where the database has been shut down. This is also called a cold backup. The database is guaranteed to be in a consistent state because no one can possibly be using the database; it is down. An inconsistent backup is taken when the database is up and running. This is also called a hot backup. While the backup is being performed, the database can still undergo change. A datafile in your backup can have old transactions and new transactions. This means the datafile is not consistent with a single point in time. Oracle needs to use special mechanisms to handle this inconsistency. One mechanism Oracle uses is the archived redo logs so that transactions can be replayed during recovery.