Combining them literally gives you: “not engaged in proper occupation.” This paints a very clear picture of someone ignoring their primary responsibilities.
不务正业 is deeply rooted in traditional Chinese, particularly Confucian, values that prioritize duty, social roles, and collective responsibility. A “proper occupation” (正业) isn't just a job; it's a stable, respectable path that allows one to contribute to the family and society. This path traditionally included securing a good education, getting a stable government or professional job, and starting a family. To deviate from this path for something considered frivolous (like art, music, or a risky startup) could be seen as a selfish dereliction of duty.
This idiom is extremely common in daily life, though its severity can vary.