What is the butterfly effect and is it more than just a metaphor?

Most people know the idea: a butterfly flaps its wings in Brazil and causes a tornado in Texas. But is that actually what the butterfly effect means, or is the real concept something more precise and more interesting? What did Edward Lorenz actually discover in 1961 when a tiny rounding error in a weather simulation produced a completely different outcome? What is chaos theory and why does it mean that even perfect knowledge of the rules governing a system cannot always predict its future? And where does the butterfly effect actually show up in the real world beyond weather, in economics, biology, or even everyday life?