When the routing is activated via Settings > Miscellaneous > Hide conversation of other agents agents see only their own conversations and can select the unassigned ones.
Agents menu: displays the agents’ menu to assign the active conversation to another agent.
Routing if offline: if the conversation is archived and the user reopens it in the future by sending a new message, if the assigned agent in the conversation is offline, the conversation is assigned to another online if there is at least one, otherwise to no agent.
View unassigned conversations: allow agents to view the unassigned conversations, when an agent replies the conversation is automatically assigned to him and the conversation is removed in real-time from the admin area of the other agents. Check this option to enable the manual routing.