What does it mean to be “in the black? ”

From the accounting perspective, if an account is said to be in the black, that means the account contains money. If a company is said to be in the black, that means that the company is making profits. Thus, generally to be in the black means to be financially well off, that is one is not in debt. 
To be in red is the opposite of to be in black and it means that the person is in debt.