The term tile store or offline tile store will be also used for this kind of store.
A mapstore layer consists of a directory with the name of the layer. This is a direct subdirectory of MGMapViewer/maps/mapstores.
In a mapstore all tiles are stored in a single sqlite database file, which has the file extension ".mbtiles". The format definition is available via github. If you have a prefilled database file, place it in the store directory. You can find examples of such tile stores on openandromaps: The overview maps are in this format. They are well suited as background maps.
Alternatively you can provide a configuration file with the fix name config.xml, which allows to fill the store for a selected area. The difference is that you need to trigger the download manually for a selected area using the bounding box feature. Such a mapstore could contain a "normal" map (e.g. downloaded from mapnik), but it could be also something like an overlay heatmap, generated from whatever data.
Here you can find more samples for configuration files.