Meanings
To be required to, ought to, expected to
Example: "I am supposed to report to the police every week."
Example: "Paul is supposed to call his mother every day."
To be permitted to.
Example: "I am not supposed to smoke there."
To be expected to; to be capable of (used to indicate that an expectation is impossible or unreasonable in the context).
Example: "How am I supposed to work in all this racket?"
Example: "What was he supposed to do—just sit there and do nothing?"
To intended to; to be expected to; to believed to.
Example: "It's supposed to rain."
Example: "The thief is supposed to be hiding in the forest."