There's a few things that would cause a problem in your upload. There's nearly 4000 polygons in this shapefile, substantially over the 1000 record limit for importing into a web map. It's not really advisable to have so many polygon features in a webmap anyway, as performance is not likely to be good (search for other threads in this forum and on the ArcGIS Online forum for more info on this issue). So consider what data you're trying to show, and if it's a lot of features, having a web service of the data would be a better way to go.
There's also a few other things - the file should be a .zip file (as far as I know, .rar is not currently supported), and the shapefile should be in the root of the .zip file, not within a folder (there's a folder called 'untitled folder' within your .rar for example - this structure would not work). Your .prj file is not part of the shapefile - .prj files must have the same base file name as the rest of the files in the shapefile - in your case that would be Export_Output_2.prj. In addition, I'm not sure, but from trying to import this in ArcMap, your shapefile may not actually contain data in the coordinate system that you have in the Greek.prj file. You should ensure that the prj has the correct coordinate system for the data that the shapefile contains - when you import into Explorer Online, the service will then automatically reproject the data into the same coordinante system as the map you're importing in to.
Hope this helps some,
