Mayn't is a short way to say may not. You glue not onto may and get this little word. It can mean “you are not allowed” (“You mayn't go”) or “it is not possible” — the same two jobs that may not has. People used it more in older British English. Though actually, almost nobody says it now. In speech and in school writing, may not in two words is what people expect. You will still meet mayn't in old books, or when someone is being old-fashioned on purpose. It is the same kind of short form as can't and don't, only much rarer — closer to shan't, which also feels old. Do not mix it up with maybe, which means “perhaps”.