This is a popular catch phrase from the original Star Trek (infused into modern culture by it’s countless reruns) that is used as a pronouncement that something is no longer alive or working. Not only in just a physiological way, but also in an other mechanical, electrical, physical, or temporal sense not related to a biological system. As such, it has expanded from using the personal pronoun “he’s” to the general non gender pronoun “its” that might also could be humorously describe some unspecified alien life form at the same time (and hence a joke), though Dr. McCoy was careful to assign gender when he said the phrase. It represents something that needs a formal pronouncement that only a kindly, but yet firm and incorruptible country doctor could offer, as others stand around clueless, wondering what has happened or what needs to be done next. That, and the fact the viewer has no way of telling by themselves and need to be told outright. Most often seen with a comma after the “It’s dead” it truly represents the slow delivery and dramatic pause, as he looks up, given by the actor DeForest Kelley, with a very serious tone of voice.
As an example of it’s increasingly widespread usage,
http://wordpress.org/support/topic/the-enable-capsulecrm-is-missing
http://futurelawyer.typepad.com/futurelawyer/2014/01/its-dead-jim.html
http://evilspeculator.com/?p=6244
http://social.technet.microsoft.com/Forums/windows/en-US/be98e588-6bfd-4f68-9139-dd34b816dca2/its-dead-jim-boot-fails-without-errors?forum=w7itprogeneral
https://www.youtube.com/watch?v=Uv1OKw5aP80
https://www.youtube.com/watch?v=aqG7nG3TJtc