In Institutes 2.9.2, Calvin says what he means by “the Gospel”: “[Jesus Christ] has in his flesh completed all the parts of our salvation.”
By the Gospel, I understand the clear manifestation of the mystery of Christ. I confess, indeed, that inasmuch as the term Gospel is applied by Paul to the doctrine of faith (2 Tim. 4:10), it includes all the promises by which God reconciles men to himself, and which occur throughout the Law. For Paul there opposes faith to those terrors which vex and torment the conscience when salvation is sought by means of works. Hence it follows that Gospel, taken in a large sense, comprehends the evidences of mercy and paternal favour which God bestowed on the Patriarchs. Still, by way of excellence, it is applied to the promulgation of the grace manifested in Christ. This is not only founded on general use, but has the sanction of our Saviour and his Apostles. Hence it is described as one of his peculiar characteristics, that he preached the Gospel of the kingdom (Mt. 4:23; 9:35; Mark 1:14). Mark, in his preface to the Gospel, calls it “The beginning of the Gospel of Jesus Christ.” There is no use of collecting passages to prove what is already perfectly known. Christ at his advent “brought life and immortality to light through the Gospel,” (2 Tim. 1:10). Paul does not mean by these words that the Fathers were plunged in the darkness of death before the Son of God became incarnate; but he claims for the Gospel the honourable distinction of being a new and extraordinary kind of embassy, by which God fulfilled what he had promised, these promises being realised in the person of the Son. For though believers have at all times experienced the truth of Paul’s declaration, that “all the promises of God in him are yea and amen,” inasmuch as these promises were sealed upon their hearts; yet because he has in his flesh completed all the parts of our salvation, this vivid manifestation of realities was justly entitled to this new and special distinction. Accordingly, Christ says, “Hereafter ye shall see heaven open, and the angels of God ascending and descending upon the Son of man.” For though he seems to allude to the ladder which the Patriarch Jacob saw in vision, he commends the excellence of his advent in this, that it opened the gate of heaven, and gave us familiar access to it.