The Activation Preference Number of a mailbox database in Exchange Server 2010 is a number specifying the preference value of that database copy. You can select the database that has to be backed up by specifying its Activation Preference Number through the Database Filter.
The original database in a Database Availability Group (DAG) always has a Activation Preference Number of 1. During database activation, when multiple database copies satisfy the criteria for activating, the Activation Preference Number is used to decide which database copy is to be activated.