A deficit is a lack or shortage of something or, more properly put, a deficiency of something. It means you haven't enough to meet the expected balance [that is, a neutral state relative to the context]. A sports team that is running behind on score, a company that doesn't have the profits to meet expenses, a politician who is lacking in morals. A deficit is a negative, relative to the objective, rather than being a small amount of something (which is still a positive).
In short, if someone says they have a deficit of money, then they're saying that they're not only out of money, but that they also have debts that their current resources won't cover.