Available - You're online and available to other users.
Away - You're online, but you've had to leave for a few moments so this is just to notify others users that you'll be back soon.
Do Not Disturb - You're online and you are notifying other users that you're busy.
Invisible - You're online, but you're showing as offline.
Offline - This will log you out the chat system overall. If you want to go back into the chat you need to click "Go online" which can be located in chats or group chats.
If you click on the pencil icon next to your current chat status, you can also make a custom status too.