They are a protest party. Being right-wing is incidental here – they appeared out of nowhere, gained support fast due to unforeseen political circumstances, but they don't exactly have a mature political agenda. They're most likely no new NSDAP, but who says we'll be that lucky every time protest parties sprout up?

The CDU moved more into a more left direction under Merkel, so there are politicians who will try to capture the more right-wing voters who don't feel themself represented by the CDU anymore. Voila - AfD is born. As a German I don't like the AfD but really don't worry about it.