Note: There is a w/u titled "mail bomb" that somewhat covers this, but I think there is a very clear distinction between a conventional "snail mail" bomb and an e-mail bomb. That is why I've created THIS w/u- to make that distinction clear.
A conventional mail bomb is a thing of terror and I pray that no one here ever gets one. It can be devastating and deadly and the intended recipient is likely to not survive. Conventional bombs sent through the postal service usually contain explosives and are small packages. Nowadays, I would include letters containing deadly viruses and deseases such as Anthrax or Ebola to be mail bombs. Simply because a bug-laden letter doesn't immediately explode with fiery results does not make it any less deadly or terrifying.
An e-mail bomb, however, is never deadly and can be classified as merely annoying. Yes, it's time consuming and frustrating, but not particularly lethal. I got one this morning in my hotmail account. 1,400 messages from the same advert company- perhaps their outgoing servers went on the fritz or maybe I'd somehow pissed someone off at that company. Whatever the reason, I was not happy to see my Inbox filled to the brim with these messages.
The way an e-mail bomb is executed is by simply sending multiple copies of the same e-mail message to the same recipient. It's like a flood of e-mail that seems to run on forever and cleaning it out of your Inbox can be a severe drag. It is meant to annoy and frustrate, usually the recipient being a twit or annoying asshole themselves.
If you've ever gone to a newsgroup and seen listing after listing of the same message on that group's server, then you've seen what basically boils down to an e-mail bomb. In newsgroups it is called a "flood" and it is just as annoying.