When you are signed in to Yahoo! Messenger or Chat, other Yahoo! members will see a dot next to your ID, indicating that your online status. You will see the status indicator next to the name or ID at the upper left in Yahoo! Mail or Yahoo! Business Email

A gray dot next to your ID means that you are offline, have logged out of Yahoo!, or have set your status as "Invisible to Everyone". If someone tries to send you a message when you are offline, you can retrieve that message the next time you sign into Yahoo!.

A yellow dot indicates you are online and can receive messages.

A red and white dot indicates you are online and can receive messages but are "Busy".

See: How do I control my availability to chat in Yahoo! Messenger in Mail?