By default, when one of the operators is online, new chats are equally distributed among the operators and assigned to them automatically. You can disable automatic chat assignment in Settings → General.
When all operators are offline, new chats become "Unassigned." An unassigned chat has an icon with a crossed operator. All operators can see it under the "My chats" tab until one of them takes a chat. To join an Unassigned chat, start typing or just press