If someone told you back in 2008 that one day they would re-tweet you, you would have probably called a doctor and stayed with them until such time as the emergency services arrived. The word sounds bizarre and even a little bit embarrassing, but it has become common currency among Twitter users. Essentially, a re-tweet is when someone picks up on a "Tweet" you have made and, attaching your Twitter ID by means of an @ sign, lets their own followers know what you have said. Depending on how large their number of followers is, it could get you quite a lot of attention. 

This occasionally leads to the phenomenon of users writing Tweets which are obviously designed to be re-tweeted, usually ones which deal with a topical issue and are at least passably funny, or at least thought-provoking. The upshot of this is that some users have "feeds" (lists of Tweets) that are made up almost entirely of re-tweets. This type of follower gets un-followed very quickly by a lot of users, who are generally sick of reading the same thing repeatedly. 

Re-tweeting is one way in which messages can spread from a single account to multiple feeds in a very short space of time, and is often used by political parties or commercial enterprises to drum up publicity in a very short space of time for little or no cost. Many people, though, will continue to wish it was called something other than "re-tweeting", for what it's worth.