If you are creating an Availability Group in SQL Server 2012 using the New Availability Group Wizard in SQL Server Management Studio, you might not realize some of the background tasks that the wizard performs when it performs its validation steps.  One of those steps is to create a temporary database on the current server that has a name in the format of [HADR Seeding Test <UniqueIdentifier>], which is then backed up to the network share location specified, and then each of the secondary replica‚Äôs attempts a restore of the backup from the network share to validate that the appropriate permissions exist for the service accounts to the share.  This can all be seen in the Default Trace information on each of the servers.

The Default Trace from the server that the wizard is being run against as the Primary will show:

The Availability Group Wizard and the HADR Seeding Test Database   image thumb

The secondary replicas being configured will show:

The Availability Group Wizard and the HADR Seeding Test Database   image thumb

This is strictly an artifact of how the wizard validates the configuration being provided to ensure that it will be able to successfully create the Availability Group.  If you create the Availability Group from scripts or through PowerShell and manually perform the backup/restore operations this database will not be created.