Twitter is a social media platform. Users tweet(send messages in a timeline) that are 140 characters or less. The benefit to the small size of the tweet is that one must condense more into less. and users who read those tweets can do so quickly.
Twitter also has some communication conventions where you can publicly or privately send messages directly to other users. It's also a great tool for finding content by topic. Unlike facebook which fronts as a personalized network social media platform(but isn't, necessarily) Twitter is a forum with intention for broader conversation. Interacting with musicians, politicians, authors, and people you just find generally interesting is easier.
Think of your twitter profile as a movement where your number of followers is determined by how interested they are in your "propaganda." (which is your tweets). You are a part of someone Else's movement when you follow them.