Users 'follow' contacts, celebrities, etc feed of 140-character messages. Messages can be targeted at users (e.g. @username) or tagged to simplify searching ('hashtag' - #topicname). 'Tweets' can be shared/repeated by 'retweeting' (RT). Twitter has a high compatibility with mobile devices and SMS enabling frequent updating and checking.
The technology behind Twitter is used elsewhere in 'Sister' websites such as Twitterfall (enables tweets to be displayed as a cascading, real-time feed) and other platforms (such as desktop-based).
Has a media/celebrity focus but has been used to communicate breaking news globally over very short time scales.
Science on Twitter
Exemplar science Twitter accounts include: (taken from Twitter 'suggested feeds' page)