To understand where an electron is, you have to look at it. To look at it, you have to shine a light on it. But when you shine a light on it, that disturbs where the electron is.
[Which is implied but nor strictly elucidated in Michio Kaku's statement; IGTU]
So, the very fact of observing an object changes its location. Therefore, he realised that uncertainty is an essential part of his picture.
[... The uncertainty principle:]
The more you know about a particles position, the less you can know about its speed and direction ... The more you know about a particle's speed and direction, the less you can know about where it is at any given time.
[At this point, Heisenberg] realised he could merge the [Classical] Schrödinger picture with the Bohr-Heisenberg picture to give us the modern day theory of the Quantum principle. In other words: the electron is a point particle, but you don't know quite where it is. And the probability of finding it at any given point is given by a wave — the Schrödinger wave. So, we now have a beautiful synthesis of waves and particles.
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