To impress upon the people the holiness of God and the impossibility of drawing near to him without a mediator, a Saviour, an atonement for sin, this instruction was given. The whole area was put out of bounds to man and beast on pain of death.
What fearful over-familiarity is seen in the way some worship the Lord today. God is dragged down to the human level and treated as if he was only a little different to ourselves. Human beings are not careful to worship God in the way he has prescribed, and instead come casually, carelessly, without any fear of God. His grace is turned into an excuse for shocking lack of reverence. The reality is that God taught mankind about his holiness and unapproachability before he sent Christ into the world. Grace is built on the foundation of the awesome holiness of God, and grace is so wonderful because it allows us to approach one who is so infinitely separated from evil. We come boldly, but we keep in mind what the Lord has told us about himself in that previous dispensation, and we continue to have awe for God. Grace should not be viewed as something which cancels the holiness of God, but which matches the holiness of God in its immensity. God does not intend that we forget about his holiness as we draw near, but that we strive to be holy as he is holy.