It's an indication the message has been read.
That means that the user logged into School Loop and viewed the message. LoopMail also sends out email notifications when a message is sent. It is possible that others also have read the message, but did so in their email without logging into School Loop. In that case, they wouldn't show a green check mark, even if they did read the message. The check mark is only for users who saw the message inside our website.