What is the difference between the status 'Processed' and 'Delivered' for the recipients of an email campaign?

Once you have sent an email campaign, you can see the status of the email for a specific recipient.

Processed: This means that your email campaign has been properly sent by Piggy's server to the relevant recipient. However, we will still wait for a status update from the server before we change the status. In any case, you don't have to worry about this status. The mail has been sent correctly to this person.

Delivered: If this status is visible, it means that the email has been delivered to the recipient. 

This does not automatically mean that the recipient has also opened the email. You can see this in the column that is displayed next to it.