An improper belief is a belief that isn't concerned with describing the territory. A proper belief, on the other hand, requires observations, gets updated upon encountering new evidence, and provides practical benefit in anticipated experience.
Note that the fact that a belief just happens to be true doesn't mean you're right to have it. If you buy a lottery ticket, certain that it's a winning ticket (for no reason), and it happens to be, believing that was still a mistake.
Improper belief is one of the subjects of the Mysterious Answers to Mysterious Questions sequence. Types of improper belief discussed there include: