If something is done incompletely, it does not have everything that should be there, or it is not fully finished. You understood the story incompletely — you missed parts. The form was incompletely filled in. The repairs were incompletely done. It is a clear, slightly careful adverb, more at home in writing and school than in quick speech, where people often say not completely or not finished. It does not mean the person is bad at their job. It only talks about how full or finished the thing is.