“Postmaster” fake emails!

I've been receiving copious amounts of fake postmaster emails recently, they're filling up my junk email folder and the occasional email is making it through to my inbox. I've checked my sent box multiple times and no emails have been sent from my account. Do these emails mean there is a beach of my security, or do these fake email addresses have access to my information? How do I stop them? What are they? Please help me, they're so frustrating and I can't get rid of this email address.

Thanks, 

Kim