A couple of notes (it's not clear to me whether you already know all of this, so sorry if I'm just repeating things you already know):

As explained by t-b, the offline "maps" downloaded for offline routing are only the "metadata" that allows routing, but not the map tiles themselves -- so routing will still work, but there won't be any maps rendered, which is not much fun...

So obviously, if you want map tiles, they must be downloaded sometime when you are connected to the network. Assuming that "Map->Tile Storage->Store downloaded tiles" is set to "ON", any tile that is downloaded will be stored, and will appear again later even if there is no data connection. However, a few things to note:

1. It seems to me (?) that even when map tiles are available, modrana still first tries to download new tiles, before rendering the existing tiles; so I find that when offline, things generally work better if I explicitly tell modrana not to use the network at all (Options->Network->Network Usage->Network: don't download map tiles).

2. Note that tiles are per-zoom-level: so even if you've downloaded the tiles for a specific region, and then while offline you go back to that region, but are in a different zoom level, no map will be rendered. (It would actually be nice if modrana behaved more like mappero in this respect: mappero scales downloaded tiles from different zoom-levels to the current zoom-level, if nothing better is available...).

As explained in previous responses, in the Download menu you can download the tiles for the area around a route / track / current location / current view, and choose how many zoom levels up and down to download in addition to the current zoom level.

With the above, I am able to use modrana offline with much success.

Hope this helps!
Dov