Shouts are publicly heard over a wide area, unlike the use of the SAY command, and are reserved for times of great need or announcements necessary to be communicated over great distances.
SHOUT is syntactically the same as the SAY command. It broadcasts your message over a much wider area, however. Everybody in your local region (e.g. all across the city in which you stand) will hear you shou. It is commonly used for challenges and as a distress call. In many ways this is a fairly anonymous form of communication as the recipients of your SHOUT (which may be abbreviated to just SH) will see your message appear as merely an ambiguous voice, only distinguished by its pitch. Shouting is helpful in situations of genuine or dire need, or of public importance. Its regular and persistent use is discouraged, as it is prone to disturb others.
Check out HELP SAYEXAMPLE for a sample spoken conversation between Avalon players to give you an idea how communication commands work.
See: HELP SPEAKING for the main help-file on forms of communication, with HELP COMMUNICATION the non-beginner summary; HELP CALLING with details of calling channels and HELP TELLS, HELP SAY and HELP ADVICE for specifics on various ways to make yourself heard.