I think in the context of this song it's meant to mean the way one might move around the stage all cocky and full of one's self, or indeed just the way you could move around in general as in walking with a jive or a spring in ones step, in just the way that Mick Jagger might appear to do. No it is not the X factor but if you could swagger with the confidence/cockyness of Jagger it certainly would help convince the judges as long as you could sing exceptionally well and possibly have a marketable image to add to that swagger.
