Unity Catalog is more part of the control plane hence work even if your cluster are not active.
Your workspace can be attached to a Unity Catalog metastore or a Hive Metastore(legacy).
As explained in previous response the data pane is where you could browse the Unity Catalog Metastore seeing all the Catalogs/schemas/Objects you are allowed to see.
The data and metadata attached to the Unity Catalog are physically hosted by default in a storage location defined at the creation of the metastore. This default storage can be override for each layer of the metastore (catalog, schema and objects).