Usually it means they just need a warm body for the task at hand. It's usually a job that requires no thinking and/or its something that includes repetition. So, let's say you want to hire someone to wait in line for you, you need someone who is willing to be a warm body, no degrees or a rocket scientist needed.
I have no idea ... I just keep hearing a korn song when I read this and not cos I like music questions... I think I desperately need sleep then cos my brain is broken cos I haven't slept much in the past 3 days :) yay korn !! ;)
Because people have opinions, whereas bodies don't, so what they really want are numbers, but the only way for those numbers to be counted is for the bodies to be warm. Interestingly when people are killed in war, they have a body count, not a people count.