Permission is when someone is allowed to do something. Obligation is when someone must do something. Prohibition is when someone is not allowed to something.
My mother gave me permission to go to the movie so I will meet you at the theater at 15:00. I am obligated to bring my sister with me although I wish my mother did not make me. I am prohibited from buying my sister candy or soda because then she will be hyper when she comes home.
In order to indicate permission, a person might use "can" or "to be allowed to."
In order to indicate obligation, a person might use "have to" or "have got to."
In order to indicate prohibition, a person might use "cannot" or "to be not allowed to."
I can go shopping with my friends. I am allowed to go shopping with my friends.
He has to call his girlfriend or she will be angry with him. He has got to call his girlfriend or she will be angry with him.
They can't come to class because they forgot their books. They are not allowed to come to class because they forgot their books.
In order to practice, imagine you are an English teacher. What rules would you create to permit, oblige and prohibit your students?
Imagine you are the king or queen of a country. What laws would you create to permit, oblige and prohibit your subjects (the citizens of your country)?