A time-honored tradition in the military and other bureaucracies. Often, it seems, the critical need for a hard-to-get or has-already-been-denied-by-the-brass item comes up, and the need is so critical that the requisitioners must selflessly sacrifice sleep to procure the item right then. This saves the quartermasters or storekeepers or whomever would normally record and check the approvals on said requisitioners' receipt of the item in question from having to work, be awake, or even be there. Quite helpful, really, of the chaps who end up doing all the heavy lifting, not to disturb the authorities.

In sum, it means to go procure in less-than-kosher means, typically in the wee hours when nobody's lookin'.