This chapter was pretty ground breaking down for me. Many times recently I have read something that has "transported me" to the destination of a road I felt I was traversing. But this chapter took me quite distinctly away from anywhere I was headed.
The concept is simply: memorials are reminders to God primarily and us secondarily. They remind/inform us that God is concerned with remembering us. The Passover is a memorial before God of His Covenantal faithfulness to deliver His people from bondage.
So also with Jesus Christ, the Lord's Supper points to the great Moses and deliverance. Our practice in church is a reminder that God's work is not finished. He judged death once to relieve it of its power and yet must still judge it again for destruction. Satan has been judged and defeated but still he awaits his final torment.
Though the Lord's Supper speaks to the church, it speaks that God desires to be "reminded" of His promises to His people. Our God enjoys when His people call to Him in dependence on His faithfulness.