If you would like to delete any of your messages, first click the checkbox in front of the message you would like to delete and then click the blue "Delete" button. This will move your message into the "Trash" folder.
You may decide to delete all of the items in your inbox. You can delete all of your messages in your inbox on the current page by first clicking on the blue "All" link located next to the "Select" option. If you change your mind before clicking on the "Delete" button, you can click on the blue "None" link that is located next to the "All" link which will uncheck your boxes.