'You're' is a contraction of the words 'you are.' When using 'You're' with the words 'supposed to' you are making a suggestion that something you strongly believe ought to happen.
Here are some examples:
You're supposed to keep that secret.
You're supposed to let me know when you leave.
You're supposed to stop when at a red light.
You're supposed to unpack once you get there.
You're supposed to return the movies you rent on time.