A person or company is event-driven when it acts in immediate response to a stimulus. A bank that picks up signs of credit card fraud will be event-driven to stop accepting charges on that account immediately.
Complex events are the second half of the equation. They are derived by distilling the information value from many simpler data points into a few, summary-level insights (the complex events) that help you make better and faster decisions.
The main reason for the recent upsurge of interest in event processing is that it has become practical to use CEP on a near-real-time, event-driven basis. Event processing is the key to situation awareness - understanding what is going on so you can decide what to do.
It's not hard to build event-based, continuous intelligence solutions that provide situation awareness, but it requires a fresh mind-set and an understanding of the principles, design patterns and best practices of event processing.