Export administrative boundaries of a country for use with an external application

You can get all administrative boundaries in several ways:

1. You could make a call at one of the Xapi filtering by location (bounding box) and tag (admin_level). Note that the Xapi is mostly overloaded these days, check current status here.
2. You could take a germany extract, for instance from geofabrik, and extract the boundaries with Osmosis
3. If I recall right, geofabrik offers shapefiles from OSM-Data, and there might be a boundaries file for Germany in their download section , see here.
4. If you wanted only admin_level=4 and 2 you could download them with josm, but for admin_level=6 this might be too much effort.

I don't know which formats are supported by Map-Explorer, but if it doesn't support osm-xml directly you could load the osm-file into Josm and export it as GPX, which most geo-applications are able to read. There are also tools available to convert osm to shapefile. More help on this topic and alternative programs can be found in the wiki.

It can be done with JOSM, but it sohohoh difficult too explain that I won't. It so dangerous too. A novice could erase nation wide data with a single click. Always experiment such things with (J)OSM without a password and best on an alternate server. I've done it with Belgium, but it wouldn't work with Switzerland. CH don't put subareas in boundary relations (believe me as I say it :-)).

As Frederik said, your best bet is a ready made map of some kind. Look up Google with searcher like "Germany map administrative svg", best in German. SVG is important. It's a vector format that will scale very well and allow you to change the picture easily with a program like Inkscape, or change it to another format. This is my third hit, just to show you the kind of things: http://en.wikipedia.org/wiki/File:Map_Germany_L%C3%A4nder-de.svg

Use the VG2500 dataset of the Bundesamt für Kartografie and Geodäsie: http://www.bkg.bund.de/nn_149566/EN/News/01News/N2011/20110915-VG2500__04-09-2011.html