Honestly it is probably out of the scope of this thread, but there is a pretty good (and long) thread about it here:Can you elaborate on what you mean by 'mystical' and also why Presbyterians reject the bodily presence (as taught by Lutherans)?
The real presence of Christ in the sacrament of communion.
I would also take a quote from THIS article (also in that thread):
All of this raises a question. How does Calvin understand the nature of Christ’s presence in the Supper? According to Calvin the sacraments are signs. The signs and the things signified must be distinguished without being separated. Calvin rejects the idea that the sacramental signs are merely symbols (for example, Zwingli). But he also rejects the idea that the signs are transformed into the things they signify (for example, Rome). Calvin argues that when Christ uses the words, “This is my body,” the name of the thing signified (“body”) is applied to the sign (the bread).
Calvin repeatedly stated that his argument with the Roman Catholics and with Luther was not over the fact of Christ’s presence, but only over the mode of that presence. According to Calvin, Christ’s human body is locally present in heaven, but it does not have to descend in order for believers to truly partake of it because the Holy Spirit effects communion. The Holy Spirit is the bond of the believer’s union with Christ. Therefore that which the minister does on the earthly plane, the Holy Spirit accomplishes on the spiritual plane. In other words, those who partake of the bread and wine in faith are also, by the power of the Holy Spirit, being nourished by the body and blood of Christ.
This, of course, raises a second question regarding the mode by which believers partake of the body and blood of Christ. Zwingli had argued that to eat and drink the body and blood of Christ was simply a synonym for believing in Christ. Calvin begged to differ. He argued that the eating of the body of Christ is not equivalent to faith; instead, it is the result of faith. Calvin often used the term “spiritual eating” to describe the mode by which believers partake, but he is careful to define what he means. He asserts repeatedly that “spiritual eating” does not mean that believers partake only of Christ’s spirit. “Spiritual eating” means, according to Calvin, that by faith believers partake of the body and blood of Christ through the power of the Holy Spirit who pours the life of Christ into them.
Calvin also rejected the idea that we partake of the body and blood of Christ with the mouth. Not only Rome, but Luther and his followers, asserted the doctrine of oral manducation (that is, oral eating). According to the Lutherans, the body of Christ is orally eaten, but it is a supernatural or hyperphysical eating rather than a natural or physical eating. Both believers and unbelievers receive the body of Christ according to the Lutherans, although unbelievers receive it to their own judgment. Calvin denied that unbelievers receive the body of Christ at all. According to Calvin, the body and blood of Christ are objectively offered to all, but only received by believers.
According to Calvin, the Lord’s Supper is also “a bond of love” intended to produce mutual love among believers. It is to inspire thanksgiving and gratitude. Because it is at the very heart of Christian worship, Calvin argued that it should be observed whenever the Word is preached, or “at least once a week.” It should be shorn of all superstition and observed in its biblical simplicity. Calvin considered the Lord’s Supper to be a divine gift given by Christ himself to His people to nourish and strengthen their faith. As such, it is not to be neglected, but rather celebrated often and with joy.