Twitter is a popular micro-blogging web application. At its very basic it is a way for a person to share a statement of 140 characters or less. That "tweet" can be read by anyone on the internet by going to the Twitter website or by using a Twitter application on a smart phone or tablet.
One of the main reasons to use Twitter is in order to "follow" a person or organization. By following someone on Twitter, all their tweets show up on your Twitter homepage in a cascading list. Why is that neat? Because, if you choose people or organizations carefully based on your interests, you can learn about good articles to read, videos to watch, events to attend or anything else they share.
So, check out the links for information on what Twitter is and how to use it.