Multi-layer basemaps are useful in that they enable labels or other reference information to be drawn on top of other layers in your web map. Some examples of multi-layer basemaps include world imagery, light canvas, and the new oceans basemap. With these basemaps you can create a "map sandwich" with your meaty (or cheesy?) operational layers being drawn between the base (bottom) and reference/label (top) layers.
Currently there's no way to create your own multi-layer basemap on ArcGIS.com, but you can create one using the REST API using the isReference property of baseMapLayer (documented here, example here). If you're not familiar with using the API you can also create one using this app from Esri Solution Engineer Phil Holleran.
The reference layer will not always be the top-most layer in a web map. If the reference layer is tiled/cached any other layers drawn server-side (map services or "map images," tiles, etc.) will appear below the reference layer while layers drawn client-side (feature services, map notes, etc.) will appear above the reference layer. For this reason, you may consider using only the base layer of the basemap if the labels/reference info conflicts with features in your client-side layers.
Other notes about multi-layer basemaps:
- They work just fine if you add them to your organization's basemap gallery.
- The reference layer does not appear in the web map contents, but is listed on the web map item description page.