Your organisation may have multiple agents and they would definitely be handling different chats. “My Chats” show the agent the chats which are assigned to him or he has taken over from the bot. 

Following are the features available in the chat menu:

• Online Status
• Agent Assignment
• Close Chat
• Saved Replies
• Customer Profile
• Labels
• Payment
• Audio/Video Call
• Shared Media
• Chat History
• Channel Timeline
• Members
• Internal Messages
• Filters
• Add Deal