In order to delete the mailbox, you should press that appears to the right of your mailbox name, if you point the mouse cursor over it:
As soon as you press the "Edit" button, the window of editing your mailbox appears. The instructions of how to work with that window are given in the Create/Edit Mailbox section.
To delete the mailbox, you should press the Delete mailbox button located in the lower-left corner of the window. As soon as you press it, the window of mailbox editing appears as follows:
You should confirm your agreement to delete the mailbox in this window. In order to delete the mailbox, you should check the "I agree to remove the mailbox" field. The "Delete" button will become active as soon as you put the mark in that field. Press it to delete the mailbox.