Nickname: Authorize a nickname to join streams on the server.
Channel: There are two types of authorization a channel gets to stream. The first is administratively where the admin of the server sets the channel up so it 'can' have a stream. The second is this command which must be issued to actually allow a stream to be pushed to a channel. This allows channel oeprators to start and stop streams inside a channel.
Example:
/stream deauth Rick
/stream auth #lobby
Channel operators can use this command if the channel is stream enabled (via an 'as chan' command). IRCops can use this to authorize users and users can use this to authorize themselves (Just because they authorize themselves doesn't mean that they'll get permission inside a channel to get a stream).