This is another way of saying no-account. You use it of a person — sometimes of a plan or a job — that you think is worthless: they do not work, they do not keep their word, they do not count. It is very informal American English, especially in the South of the United States, and it is a hard, dismissing word. You will mostly hear it in front of a noun: that no-count boyfriend, a no-count scheme. Older speakers still say no-account; no-count is the shorter form of the same idea. Though actually, it is not the grammar word for things you cannot count, like water or advice. That is a different no-count, written in a different place.