I think this song deals with Reznor's hatred of a conformist society where everyone is forced to be the same, lined up in a great "march of the pigs" (kinda reminiscent of Pink Floyd's "The Wall"). So he urges the listener to "pick away at it, I want to watch it come down," being the pretence of our society, the need to be a follower. "Take the skin and peel it back but doesn't it make you feel better?" - you'll feel better if you peel back all the crap society has forced on you and just be yourself. Reznor also reminds that society is bigger than us and will inevitably still rule over everyone - "the pigs have won tonight they can all sleep soundly".
I think this song deals with Reznor's hatred of a conformist society where everyone is forced to be the same, lined up in a great "march of the pigs" (kinda reminiscent of Pink Floyd's "The Wall"). So he urges the listener to "pick away at it, I want to watch it come down," being the pretence of our society, the need to be a follower. "Take the skin and peel it back but doesn't it make you feel better?" - you'll feel better if you peel back all the crap society has forced on you and just be yourself. Reznor also reminds that society is bigger than us and will inevitably still rule over everyone - "the pigs have won tonight they can all sleep soundly".