The new controller seems to be extremely similar to the existing Classic Controller but has the additional shoulder buttons (found on Gamecube) and a more Gamecube controller shape.
The website states the controller will be available this summer and we'll take a guess that it'll come to European and North America shortly after.
The reason behind this new controller is mystery, it's hard to know what Nintendo are up to. It could just be so that people can play Gamecube games with this controller - or it could mean we're going to see more recent Virtual Console games - Dreamcast, Gamecube itself perhaps? or potentially it could be used for Wii games that want to use a more original shape.
Obviously we'll find out more over the next few months.