(noun) This phrase is a combination of the words swagger and dance. Swagger refers to one's comfortability aka confidence, pride, etc., with oneself, meanwhile dance is just a form of self expression through movement. Therefore the person that does the swagger dance exhibits swagger and the ability to simultaneously dance thus meaning that this person is dancing in a cool manner. The person doing the swagger dance is usually in other environments a reserved individual.
"Look at my gym coach over there dancing!"
"Oh my god, I can't believe it! He's doing the swagger dance!"