John Calvin wrote on the Supper extensively, and felt that it should be observed weekly, as do I. The following is from a paper that I’m working on in order to lead my church in the direction of observing weekly communion.
John Calvin writes that this union with Christ is a mystery and by it’s nature is incomprehensible. Through communion, God “shows its figure and image in visible signs best adapted to our small capacity.” In other words, this is a sign that we can comprehend even though we do not comprehend the union that is taking place.
The Great Theologian goes on to write, “We now understand the purpose of this mystical blessing, namely, to confirm for us the fact that the Lord’s body was once for all so sacrificed for us that we may now feed upon it, and by feeding feel in ourselves the working of that unique sacrifice; and that his blood was once so shed for us in order to be our perpetual drink.”
Therefore when we partake of His body and blood, which He bids us to do, we can conclude that the power of His life-giving death will be efficacious in us. Or in other words, the effects of His sacrifice are able to produce the desired effects in us. This is spiritual growth for the believer.
The best picture of this is from John 6:22-71. This passage shows us exactly what is taking place in the communion when we partake of Christ’s blood and body. We are in communion with Him and He is sustaining us with spiritual food. He gives His life for His sheep. What better way to represent that, in His provision for spiritual life by giving us His spiritual body.
This passage in John 6 shows that it is a spiritual feast for verse 63 points that the event is something spiritual: “It is the Spirit who gives life; the flesh profits nothing. The words that I speak to you are spirit, and they are life.” Jesus is saying that all that He is saying is of a spiritual nature, not a physical one.
We now understand the purpose of this mystical blessing, namely, to confirm for us the fact that the Lord’s body was once for all so sacrificed for us that we may now feed upon it, and by feeding feel in ourselves the working of that unique sacrifice; and that his blood was once so shed for us in order to be our perpetual drink.
In view of John 6, Calvin writes, “Once for all, therefore, he gave his body to be made bread when he yielded himself to be crucified for the redemption of the world; daily he gives it when by the word of the gospel he offers it for us to partake, inasmuch as it was crucified, when he seals such giving of himself by the sacred mystery of the Supper, and when he inwardly fulfills what he outwardly designates.”
What is eating and drinking of Christ doing? It is looking to Him for our sustenance as opposed to other means for our spiritual growth. Just as wine and bread sustain our physical bodies, so does partaking of communion sustain our spiritual lives.
 Institutes, IV, XVII, 5.