This is a new feature that serves as extra storage for inventory units that are not being used in a party. Units of all types can be sent to Reserves.

You can select multiple units to be sent to Reserves at once. There is also a setting to automatically send units to Reserves immediately after being summoned.
You can access the additional settings for this feature from the Home screen by tapping Menu > Options and finding the "Automatic transfer of obtained units to reserves" section.