If I remember rightly, this happens because you only think it's full. When he takes out the three squares, there are gaps in the rectangle left behind but they are too small to notice. They add up to the size of the three squares. It's essentially the same as this:
If you drew a line from corner to corner, essentially drawing the hypotenuse, you'd find that in the top triangle, the hypotenuse isn't straight but curves in. This means there's a "gap", but it's too small to be seen/noticed. If you look at the bottom triangle, the hypotenuse is straight and the "filled in" bit is from the missing square:
