Illusion of continuity
What they mean, is that our experience is assembled from hints presented by the sense organs. The eyes, ears catch glimpses of what's going on, esp. as we move around - and then build a theory from those hints, theory that we see as reality. There's a lot of assuming going on during that process, a lot of interpretation, and a lot of habit.

EDIT

Once you "let go" enough, you start seeing it. By "let go" I mean the unconscious process by which we maintain our contrived world. Nowadays I see it at both micro and macro level. For example as I hold the cup and look at it I can see how the mind "grasps" the "signs" - raw momentary snapshots of some distinct features, and how it "tells" itself what these signs imply by inferring the cup from them. I see how the mind goes over these "signs" again and again in circles, telling itself the story of the cup. Similarly, at the macro level, I can see how the mind grasps the facts of the world and builds the narrative of my life from these.

When some people practice mindfulness, they practice the opposite of letting go. They think mindfulness is when your observation is watertight. But watertight observation is really just a tighter version of the assembly process by which we contrive the world. Instead, as you stop trying to be in control of experience, you start seeing the gaps in the model. These gaps is what we are after - but you can't contrive your way into them, you can't control it - it only comes from letting go, which involves handling tremendous amount of insecurity.

EDIT2

What @xxxx means with his "looking for keys" analogy: normally the way our mind works is, we get a hint from sensory organs, we build a hypothesis of what we are looking for/at, and then we validate it by examining the evidence from sensory organs. If we approach meditation with the same attitude, we would say to ourselves: hey, I must be looking for gaps in experience, gaps in the modeling process, and here is how it's supposed to look like. But you can't see the real gaps with this attitude, this would be contriving gaps with your mind, like dreaming yourself a dream. Instead, it comes from letting go of the inner dialog, of re-telling yourself the story of what you see (micro), and the story of your life (macro).