[A] second development in English Calvinist thought, also international in its scope, was the rising importance of federal theology. Federal theology built upon the covenant theology of the Reformers, especially that of Heinrich Bullinger, Zwingli's successor of at Zurich, and also of Calvin. For Bullinger, God had made one covenant with humanity, the covenant of grace, known by anticipation in the times of the Old Testament and by remembrance after the coming of Christ. For Calvin too there was but one covenant, that of Grace, but he stressed its testamentary character whereas Bullinger spoke of it as more conditional, although for both the covenant was the means in a history of salvation by which God unfolded his purposes. At the end of the sixteenth century, the Heidelberg Reformed theologians Zacharias Ursinus, Caspar Olevianus, and Franciscus Junius shaped the idea of a covenant of works distinct from and preceding the covenant of grace. Important English Calvinists, beginning with Dudley Fenner and including many later Puritans, adopted this double covenant federal theology with its covenant of works made with Adam, the federal head of humanity, to be followed, after the fall of Adam, with the covenant of grace, which was anticipated in Moses and fulfilled in Christ, the federal head of redeemed humanity. This federal theology was not only a pedagogically useful and biblically warranted scheme for organizing theology but also "a useful vehicle of the gospel message," closely related to the flowering of Calvinist piety. [Dewey D. Wallace, Jr., Shapers of English Calvinism 1660-1714: Variety, Persistence, and Transformation, (New York: Oxford University Press, 2011), 16-7]
So more of a sketch here rather than a definition.
Myk Habets and I, as Evangelical Calvinists, affirm one covenant of grace as I have posted one of our Theses from our soon to be released book, here. In light of my belief in one covenant of grace (notice Dewey underscores Calvin's belief in 'one covenant' of grace too ;-), I obviously think expanding this covenantal framework into a so called 'bi-lateral' or 'two-winged' understanding constitutes a deleterious move; but one that is natural to how classic Calvinists conceive of their doctrine of God (e.g. 'two-wills' ... see John Piper's and Matt Chandler's rather infamous endorsement of this kind of thinking [although they are not into 'Federal Theology' proper, per se]). Without getting too deep into the weeds on this, and especially the respective doctrine of God behind Federal Theology; the biggest problem I see with this double covenant schema, propounded by Federal theology, is its placement of creation over against Creator. There is a dualist wedge placed between humanity, for example, and Creator; such that the unity of Christ's person in the incarnation becomes disjointed---I digress.
One of the bigger pastoral and soteriological problems I see with Federal Theology, and its dualistic conception of salvation; is that a bridge outside of the unitary person of Christ is needed to bridge the gap between a sinful humanity and a holy Creator. It is this bridge that then shapes how Jesus must act in his saving act (or the conditions of the Covenant of Works), and thus the person of Jesus as the God-Man is decoupled; the Man part trying to meet the conditions of uniting sinful humanity to God, thus impinging on the shape of the God part in Jesus. With the consequence being that the Divine Person, Jesus Christ becomes subservient to his creation, all in the name of bridging the gap between part of humanity (the elect) and God. Matt Frost, a Barthian-Lutheran theologian and friend, provided a critique of this kind of stuff in a recent comment that I think is apropos for my own critique; Frost writes:
[...] I find classical Calvinism lacking in its doctrine of the vicarious humanity of Christ because it becomes an extension of the division of God from creation, up into the godhead. If the vicarious humanity of Christ is a perpetual intercessory appeasement of the Father, we have a broken doctrine of God. There is only part of God in Christ, and part of God to be appeased by him. The vicariousness becomes Jesus doing our actions for us, and correctly, in order to please God. "Our great high priest." The whole cultic mechanism of appeasement elevated into the heavens and done for us. [see the full comment here]
Federal Theology introduces a division of God from creation, as Matt puts it, so that Jesus in seeking and saving the lost actually ends up losing his identity as the eternal Logos because he is no longer the Word over creation, but the Word subservient and under creation.
Okay, so I made it to the weeds; sorry ;-)!
Federal Theology is a historically situated scheme of thinking, but, unfortunately, there are some today who seek to repristinate or redress this schema for contemporary Christianity (I have friends who have been taken captive, to one degree or the other). I am only left to wonder why? Why do people today seek to re-present this scheme of theology when we have moved in constructive ways (and even through constructive retrieval) into constructive Trinitarian theology. Theology that emphasizes God's unity in his diversity, and theology that emphasizes God's loving and gracious way amongst us. Why would we want to go back to a theological construct that has obvious and fundamental flaws relative to how it thinks about God, and then how God must relate to his creation? I think a lot of this simply has to do with cultural forces, and lack of exposure to sound Trinitarian theology (the kind that EC tries to imbibe); more than it does with blatant disregard for thinking according to said Trinitarian theology. Which continues to provide impetus for me to write about such things online :-). amen.