Modal auxiliary verbs allow us to express notions of ability, obligation, repetition, etc. They also allow us to conjugate other verbs in tenses other than the present.
• Must: obligation, duty or certainty:
You must fasten your seat belt. You are obliged to fasten your seat belt.
Must we report this conversation to Bruno? Do we have to report this conversation to Bruno?
Somebody is knocking on the door, it must be Bob. Somebody is knocking on the door, I'm sure it's Bob.
• May: uncertainty, probability, possibility:
We may arrive late tonight. Don't wait for us. It's possible that we will arrive late tonight. Don't wait for us.
May I talk to you for a minute sir? Could I talk to you for a minute sir? (formal)