For each server listed in the ESM, there is a folder called Queues. It displays the status of all connections the Exchange server is attempting to make. It will show the number of messages waiting to be sent. For any of the individual messages, you can see the sender, recipients, subject, and size. You can also see if a particular message is a Non-Delivery Report (NDR).
Messages that stay in the queue typically indicate a transmission problem. It could be that the destination domain doesn't exist, or that the destination domain is refusing your transmission, or that the destination domain is having a problem receiving messages. In any case, if a message stays in the queue, Exchange will attempt to send it again later.