What is this Reactive Programming Thing?

There has been a lot of hype around this word "Reactive Programming" whether it's with the [Reactive Manifesto](http://www.reactivemanifesto.org/), [Reactive Streams](http://www.reactive-streams.org/), the [Coursera Course on Reactive Programming](https://www.coursera.org/course/reactive).  What does this word Reactive *really* mean?  The dictionary describes it as "readily responding to a stimulus".  Yeah, that's useless.  Instead of a bunch of handwaving, let's break it down into some small concepts and how we can relate it to programming that we're already doing.  Maybe instead of "Reactive Programming", we just call it "Composable Event Processing" or something even better.  You help name it!