What is the unit dead load of concrete?
I am going out on a limb here, but I think I understand what it means. 

A cubic foot of concrete weighs 145 lbs. Therefore its deadload is the same, as part of a component of a building that an engineer needs to consider how strong a particular part may need to be to hold up over time.
In this case, for concrete, the unit of measure is cubic feet. If the material was 2X framing, then the unit of measure for the deadload would be by the foot for each dimension of lumber, 2X4, or 2X6 or 2X8 and so forth. With plywood, the unit of measure would be square feet. It would also be adjusted for the various thickness of each plywood thickness available.
So in a nutshell, each building component or part has its own unit of measure, therefore, its own unit of dead weight.