Worthlessness is a state of being unimportant and useless. When you complain about your coworkers' worthlessness, you're talking about the fact that they don't contribute anything at work.
The noun worthlessness can describe an object's lack of value, but it's more often used to describe a person — especially the way she feels about herself. For example, a depressed person might struggle with feelings of worthlessness — of not being useful or important in any way. The adjective worthless is at the root of worthlessness, with its meaning of "without value." Both words come from the Old English weorþ, "significant, of value, or appreciated."