Calvinist Louis Berkhof explains the difference between incommunicable and communicable attributes:
4. The most common distinction is that between incommunicable and communicable attributes. The former are those to which there is nothing analogous in the creature, as aseity, simplicity, immensity, etc.; the latter those to which the properties of the human spirit bear some analogy, as power, goodness, mercy, righteousness, etc. This distinction found no favor with the Lutherans, but has always been rather popular in Reformed circles, and is found in such representative works as those of the Leyden Professors,[ Synopsis Purioris Theologiae.] Mastricht and Turretin. It was felt from the very beginning, however, that the distinction was untenable without further qualification, since from one point of view every attribute may be called communicable. None of the divine perfections are communicable in the infinite perfection in which they exist in God, and at the same time there are faint traces in man even of the so-called incommunicable attributes of God. Among more recent Reformed theologians there is a tendency to discard this distinction in favor of some other divisions. Dick, Shedd, and Vos retain the old division. Kuyper expresses himself as dissatisfied with it, and yet reproduces it in his virtutes per antithesin and virtutes per synthesin; and Bavinck, after following another order in the first edition of his Dogmatics, returns to it in the second edition. Honig prefers to follow the division given by Bavinck in his first edition. And, finally, the Hodges, H. B. Smith, and Thornwell follow a division suggested by the Westminster Catechism. However, the classification of the attributes under two main heads, as found in the distinction under consideration, is really inherent in all the other divisions, so that they are all subject to the objection that they apparently divide the Being of God into two parts, that first God as He is in Himself, God as the absolute Being, is discussed, and then God as He is related to His creatures, God as a personal Being. It may be said that such a treatment does not result in a unitary and harmonious conception of the divine attributes. This difficulty may be obviated, however, by having it clearly understood that the two classes of attributes named are not strictly co-ordinate, but that the attributes belonging to the first class qualify all those belonging to the second class, so that it can be said that God is one, absolute, unchangeable and infinite in His knowledge and wisdom, His goodness and love, His grace and mercy, His righteousness and holiness. If we bear this in mind, and also remember that none of the attributes of God are incommunicable in the sense that there is no trace of them in man, and that none of them are communicable in the sense that they are found in man as they are found in God, we see no reason why we should depart from the old division which has become so familiar in Reformed theology. For practical reasons it seems more desirable to retain it.
Berkhof, Louis (2014-02-23). Systematic Theology (Kindle Locations 1102-1123). . Kindle Edition.