Supposed means ought to or expected. If you are supposed to go to your grandma's house for dinner, then your grandmother expects you.
When you're supposed to do something, you either should do it or people expect you to do it. You are supposed to go to the doctor (and dentist) for a check-up once a year. You're not supposed to jaywalk. If you make a plan with friends to go to the movie, you're supposed to show up — your friends expect you. Also, supposed can mean something that's doubtful, as in "I don't trust this criminal's supposed alibi."
