First, we must attend to what a sacrament is. It seems to me, then, a simple and appropriate definition to say, that it is an external sign, by which the Lord seals on our consciences his promises of good-will toward us, in order to sustain the weakness of our faith, and we in our turn testify our piety towards him, both before himself and before angels as well as men. We may also define more briefly by calling it a testimony of the divine grace toward us, confirmed by an external sign, with a corresponding attestation of our faith towards Him. You may make your choice of these definitions, which, in meaning, differ not from that of Augustine, which defines a sacrament to be a visible sign of a sacred thing, or a visible form of an invisible grace, but does not contain a better or surer explanation. As its brevity makes it somewhat obscure, and thereby misleads the more illiterate, I wished to remove all doubt, and make the definition fuller by stating it at greater length. (Institutes, 4.14.1)Notice how he walks through the debate unscathed.
A sacrament isn’t purely supernatural, and definitely not something facilitated by the power of a priest. Yet the more important (call it the first) definition is supernatural, for it has to do with what God does do us. The Lord seals on our consciences his promises of good-will toward us. The Lord is active in the sacraments; He is the subject of the sentence above. God, through the inward working of His Spirit, uses sacraments to give us confidence in His promise of redemption. A simpler way to put it is that God increases our faith through the sacraments. It is exactly the same function as His Word. Indeed, Calvin goes on to stress the inseparable connection between the Word and the sacraments.
Notice however the secondary definition: we in our turn testify our piety towards him, both before himself and before angels as well as men.
Calvin does not deny that the believer also brings something of value: his testimony.
Of course, modern evangelical Protestantism has all but forgotten the first part of Calvin’s definition and accepts (implicitly in spirit, if not explicitly in their doctrinal statement) only the second part. I mention this because many might agree in principal that God is active in baptism or communion, but they trivialize what is meant by a “seal”. The primary actor in the sacrament is always the believer. Baptism is a person’s public testimony. And oh yes, I almost forgot, God seals us.
You see clearly how Calvin walked between Luther and Zwingly—staying closer to Luther.
We do come to the sacraments/ordinances to exhibit our faith. But we also come to have our faith renewed and increased through the outward signs of God’s promise.