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.
Some commonly used auxiliary verbs:
• CAN: ability to do something, possibility or permission:
Horatio can smell an animal in the jungle from miles away. Horatio is able to smell an animal in the jungle from miles away.
Susie can't come today. Susie is unable to come today.
Can I borrow this pen? Will you let me borrow this pen?
• WILL: the future or wishes:
Bruno Delavigne will be here tomorrow. Bruno Delavigne is going to be here tomorrow.
I won't call him anymore. I don't plan to call him again in the future.
Will you stop making noise please? Please stop making noise!
• 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)