One of the things he mentioned is that science fiction writers have not yet used the theory of imaginary time in their plots. When asked why they haven't, he answered, "Because they don't understand it."
Definitely, imaginary time can be difficult to grasp. Imagine a line drawn on a piece of paper. At the far left end of that line is the "past" and at the far right end is the "future". In the middle is the "present". When you began reading this post, you were in the present but by the time you got to this paragraph, the reading of the first paragraph is already in the past. What you haven't yet read is in the future.
Now turn that solid line on the piece of paper into a cross, right down the center. Imaginary time is that vertical line. In positivist philosophy, along that vertical line are things we are present to witness as well as those we have not witnessed but we believe to exist anyway. For example, as you're reading this, you might be aware of your computer or mobile device, the room in which you're sitting or standing, sounds in the background - perhaps a television set, the air conditioner, overhead fans, traffic outside... All of that is time that you are witnessing.
Now consider a loved one - your father, mother, spouse, children, etc. They are not in the room with you at present and yet they are living out their own present elsewhere. That is the vertical line. It is all that is currently happening in the present that we do not witness ourselves and yet we believe that it exists.
Stephen Hawking takes this theory to an entirely new and complex level. In the Big Bang theory, for example, the universe began in an instant so miniscule that it could not be measured. It simply exploded into being. The explosion itself is still causing all matter in the universe - stars, planets, and all else - to move further and further apart. Prior to the Big Bang, there was no time because there was nothing but empty space.
But other physicists theorize that the Big Bang that created our universe is only one of billions - that all stars die and when they do, they first are compressed into an area that perhaps would fit on the tip of a needle - before exploding into something our minds can't even fathom, like thousands or millions of atomic bombs. With each explosion (and they occur every day) new matter is formed, along with dark matter and dark holes.
In quantum physics, if you return to that vertical line on the piece of paper, it theorizes that billions upon billions of things are occurring at this exact moment, even though you can't witness it directly. This could mean that there are countless universes, parallel worlds... even worlds that are just beyond our noses but we can not witness them with our physical bodies and capabilities, just as we can not witness what is going on in a different geographical location but we believe that life carries on there nonetheless.
To a science fiction writer, the theory of imaginary time presents a myriad of possibilities, by leaping through to different worlds or watching events unfold simultaneously. The question would then be if the horizontal line shows the past, the present and the future, how would those simultaneous events along the vertical line impact the future? To write such a science fiction plot would require advanced knowledge of the theory of imaginary time; something Isaac Asimov could do with seeming ease.
If you're interested in an interview with Stephen Hawking where he talks about imaginary time, artificial intelligence and more, here's a video below: