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1.
When a twitter user has a one-way conversation with a celebrity so that to the users followers, it seems like they are talking to a celebrity and thus are instantly über-cool in the eyes of their followers, when in fact they are a loser with nothing better to do than have a fake conversation with themselves.

Similar to name dropping IRL, but even more annoying and even less likely to be true.
Tweet-Dropper: @BritneySpears How did the barbecue go? I heard Justin Timberlake was there too >.< awkward?

Tweet-Dropper (A few minutes later, without a reply from Britney): @BritneySpears Haha yes, I suppose after a while it got pretty normal for both of you, you must go to loads of the same things!

Tweet-Dropper (Again few minutes later, still without any replies from Britney): Yeah, it's been great! How do you squeeze so much into 140 chars lol? =P

Tweet-Dropper's Follower: Wow, this guy I'm following is having a conversation with THE Britney Spears!

Tweet-Dropper (To self): They are totally falling for my Tweet-Dropping!
by James Xuan April 22, 2009
 
2.
to eavesdrop on twitter conversations, without making your own comments.
I saw Stephen and Leslie on Twitter and was tweetdropping on their conversation.
by jubu the fantastic March 16, 2009