What's a Mailbox Collection?

In Migration Manager for Exchange we use a collection to manage the mailboxes to be migrated.  Depending on your migration plan you can use these collections for specific tasks or stages.  To provide flexibility, the mailboxes to be synchronized are grouped into mailbox synchronization collections. A mailbox synchronization job can handle multiple collections. Each of these collections has its settings, including the mailbox database and preferred dates for migrating the collection’s mailboxes.
Collections can be populated by specifying individual users, distribution groups and Active Directory containers.  You can preview a flat list of resulting collection members at any time.

The most common method that we see collections setup is by what stage is the mailbox in for the project.  These collections are called a "Sync" or "Switch" collection.   Mailboxes that are in the sync phase and the users are still using the source mailbox will be the "Sync" collection.   Once the user is ready to be migrated to the target they are then moved into the "Switch" collection.   This allows the the mail to sync from the source to the target while the user can be switched with little to no impact.

For steps on how to create and manage a collection you can read the document below.