"Getting" Twitter isn't really that hard. Most people understand that an e-mail is an online version of a written note or letter. But there are a few short falls of e-mail that don't match how we communicate in the real world.
First, it's difficult to have a real time conversation over e-mail. Second, people usually do not talk to each other by speaking several paragraphs before getting a response during a casual conversation. Third is the fact that you can't easily start a conversation with someone you don't know.
Twitter and Facebook simply take the conversations that we have at parties, cafes, bars and mixers into the online world.
Facebook is the private party or water cooler chat we have with the people we know, whereas Twitter is the place to have a random conversation, in public, usually with strangers. The beauty of Twitter is that you can search the conversations and jump in at any time.
Just like many people don't go to bars or cafes for atmosphere, the same is true for logging onto Twitter or Facebook. You don't have to do it if it doesn't float your boat.