To edit an e-mail address, click the pencil icon; it's the first icon under the “Actions” column heading. This will allow you to update the name and/or the e-mail address for that member.
To delete an e-mail address, click the trash can icon in the “Actions” column. Note that once an e-mail address has been deleted, it is gone. (Of course, if you delete it in error, you can enter it again using the “Add” instructions above.)