What's the Purpose of the Psalms?

Calvin:

Although the Psalms are replete with all the precepts which serve to frame our life to every part of holiness, piety, and righteousness, yet they will principally teach and train us to bear the cross; and the bearing of the cross is a genuine proof of our obedience, since by doing this, we renounce the guidance of our own affections, and submit ourselves entirely to God, leaving Him to govern us and to dispose of our life according to His will, so that the afflictions which are the bitterest and most severe to our nature become sweet to us because they proceed from Him.

In one word, not only will we find here general commendations of the goodness of God which may teach people to repose themselves in Him alone, but we will also find that the free remission of sins, which alone reconciles God toward us and procures for us settled peace with Him, is so set forth and magnified, as that here there is nothing wanting which relates to the knowledge of eternal salvation. 

--John Calvin, 'Preface to the Commentary on the Psalms,' in Elsie McKie, ed., John Calvin: Writings on Pastoral Piety (Paulist, 2001), 58