Invariably, you will get some bounced emails. Bounces can happen because of bad email addresses, server outages, a full inbox, or a bad sender reputation, and many other reasons. Whenever an email bounces, it gets stored in your email bounces list and must be processed. You cannot send to any email that is on this list.
So what is meant by 'processed'?
To keep you from continually sending emails to email addresses that have bounced (a very bad practice for maintaining a high sender score), these bounced emails must be processed in the system with one of the following two actions:
Inactivate the email marks the email as do-not-email, and removes the email from all Online & Email lists. It does not remove the email or the person from your system and it does alter the record in any other way. It only keeps you from emailing this record in the future.
Remove the bounce actually removes the email address from the bounce list. This effectively allows you to begin delivering email to that address again, at least until it bounces again.
This is what is referred to as processing your email bounces.
Also see: How to remove bounced emails