The New Chats button appears at the bottom of your main chats list when you've received a message from someone you haven't talked to before.
If the button is blue that means you’ve received messages from new people that you haven’t checked yet.
If the button is grey that means you’ve viewed your New Chats but didn’t clear them. It will be blue again if another new person sends you a message.
To check your New Chats, simply tap the button at the bottom of your chats list.