The Reformed often employed a sort of communicatio idiomatum for the sacraments, applying the name of the thing signified to the sign. The obvious example is “This is my body.” In his Commentary on the Heidelberg Catechism, Zacharias Ursinus gives three reasons explaining why this is valid. Number 3 is important for understanding the term exhibitio as it pertains to Reformed sacramental theology:
There are three reasons which may be assigned why the Scriptures thus speak, interchanging the names of the signs, and the things signified. The first is on account of the analogy which there is between the sign, and the thing signified. The thing signified is according to its own nature, such as the sign is according to its nature, the opposite of which is also true: for as water which is the sign, washes away the filthiness of the body, so the blood and Spirit of Christ, which are the things signified, wash away the pollution of the soul: and as the minister applies the sign outwardly, so God by virtue of his Spirit applies inwardly the thing signified to all those who receive the sign with true faith.
Secondly, the Holy Ghost thus speaks for the confirmation of our faith through the use of the signs: for the signs used in the sacraments testify the will of God to us on account of the promise annexed thereto: “He that believeth, and is baptized, shall be saved.” But why does the Holy Ghost thus speak for the confirmation of our faith? Because in the proper use of the sacraments the exhibition and reception of the signs, and things signified, are inseparably connected. And hence the Holy Ghost interchanges the terms, attributing what belongs to the thing signified to the sign, and what belongs to the sign to the thing, to teach us what he gives, and to assure us that he does really give it.
The third reason, therefore, why such language is employed is because the exhibition of the things signified is inseperably connected with the signs used in the sacraments.
(pg. 365 of the P&R reprint)