It's not so much stopping thoughts, as it is to be able to guide your focus at will, as you said. In the end your mind isn't so much blank as hyper-aware of itself without the normal push-pull of thoughts that you described in your earlier comment. Best way I can describe it is as a place where your higher mind is at rest and your instinctive/subconscious mind is fully active.

The mystical philosophies around meditation describe it with all sorts of features and properties, but I'll skip getting into that here. I'll just mention martial arts in particular. They practice relentlessly so that the actions are instinctive, then they use meditation so that higher-brain noise doesn't get in the way of that hyper-awareness and instinctive action.