This is a quote from Bob Letham’s book The Lord’s Supper where he summarizes Calvin’s view of the spiritual presence of Christ in the elements of the bread and wine:
Christ does not come down to us in his body and blood. Instead, we are lifted up to him by the Holy Spirit. Christ, being the eternal Son of God, is of course, everywhere. Moreover, he has permanently united himself to the human nature assumed in the incarnation. In that sense, the person of Christ is present with us as we eat and drink. Yet, on earth, the Son of God was not restricted or confined to the humanity he assumed, but was simultaneously filling all things, directing the universe even as (according to the flesh) he walked the dusty roads of Palestine. So, at the right hand of God, the Son fills and directs the universe (Col. 1:15-20), now unbreakably united to his assumed humanity, while in terms of that same humanity he is limited and in one place. Yet that humanity is never separate or apart from the divinity, the eternal Son of God with whom and in whom it is one undivided person. Thus, in the sacrament the Holy Spirit unites the faithful to the person of Christ as they eat and drink the signs, the physical elements of bread and wine. There is an inseparable conjunction of sign and reality. As truly as we eat the bread and drink the wine, so we feed on Christ by faith.
Robert Letham, The Lord’s Supper: Eternal Word in Broken Bread (Phillipsburg: P&R Publishing, 2001), 28-29.
In Calvin’s own words from The Institutes of the Christian Religion 4.17.32:
Now if anyone should ask me how this takes place, I shall not be ashamed to confess that it is a secret too lofty for either my mind to comprehend or my words to declare. And, to speak more plainly, I rather experience than understand it. Therefore, I here embrace without controversy the truth of God in which I may safely rest. He declares his flesh the food of my soul, his blood its drink [John 6:53ff.]. I offer my soul to him to be fed with such food. In his Sacred Supper he bids me take, eat, and drink his body and blood under the symbols of bread and wine. I do not doubt that he himself truly presents them, and that I receive them.