Customize Email Body is a setting that allows your email body and note message be separate. By default, they will be the same. 
When 'Custom Email Body' is on, your contact will receive a different message on their email vs the note landing page. You can edit your custom email body on the edit note page. It's HIGHLY recommended you use merge fields within the custom email body. Do not manually type in the contact's name in the custom email body section.
We recommend leaving this feature off for most sends; however, use this setting if your email has a separate call to action ( ie - "click below to watch this video") then your note landing page ( ie - "click below to make a donation").
When Sending via Task Watch Out
Because tasks inherit note settings, your tasks will use your notes 'Customize Email Body' when it's turned on at the note level. Therefore, it's highly recommended you review this setting before sending via the tasks list with it enabled. Otherwise, your contact might receive a random email message that is not specific to your task.
For more information, watch the video on How do I update email settings?