How Physicists Proved The Universe Isn't Locally Real

When we sleep, we can hardly distinguish reality from a dream. So how do we know what's real and what's not?
To scientists, something is considered "real" if its properties are determined prior to being measured. For example, an apple can be green even when no one is looking at it. However, the quantum world appears to follow different rules.
Recently, three scientists won a Nobel Prize by proving that our universe isn’t locally real. But if our world isn’t real, what is this place we live in?